Mct mht ("This is my haus, nigga, my haus!" -Yao Ming to Rasho Nesterović ) 14:12, 26 August 2006 (UTC)
I am also 24.155.72.152 (talk) on a few of the math pages. Mct mht 01:50, 5 April 2006 (UTC)
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Oleg Alexandrov (
talk)
23:16, 2 April 2006 (UTC)
You are removing the assumption that some measurable functions have real values from a lot of places. But then you can't talk about almost everywhere convergence, you need values at least in a metric space.
Do you have references when those theorems hold? I suggeest you go back to the real number-valued functions, and that's the classical case, and it is surely correct. Thanks, and you can reply here. Oleg Alexandrov ( talk) 15:10, 12 April 2006 (UTC)
Yeah, in fact it is kind of weird that the previous contributors imposed the real-valued assumption. Surely something like the dominated convergence theorem, Egorov's, and Lusin's don't need that assumption. Should be in any reasonably modern introductory text on real analysis. Mct mht 19:22, 12 April 2006 (UTC)
A side note, apparently there are Lusin type results for Bochner integrals. Didn't know that. Mct mht
Hi. It seems you're still working on square root of a matrix, so I won't edit that page myself at the moment. However, could you please bear in mind that the phrase "positive matrix" is often used to describe a matrix with positive entries? I gather that you're talking about a positive-definite matrix. Great work, by the way. Cheers, Jitse Niesen ( talk) 10:01, 17 August 2006 (UTC)
Hi,
Back in August, you removed some text from resolvent formalism, and I don't understand why. Could you take a look at the talk page? linas 03:49, 27 October 2006 (UTC)
Hello. You reversed a change I made to vector space. Part of the reason why I was confident about that change was because the algebra over a field article states that the bilinear multiplication operator must be such that (ax)(by)=(ab)(x y). However, now that I look into the formal definition of bilinear, I do not see how this follows. That being said, I think that there are many important results (for example, results about commutable operators and their eigenspaces) that depend on this. It seems like there should be some stronger version of algebra that includes this property. I understand that in most cases this is a result of the commutivity of the field; however, strictly speaking the commutivity of the field should have nothing to do with ax=xa. Right? That is, a vector x need not have coordinates from the field. All I need with an algebra is some definition of scalar-vector multiplication; I can do that without having vector coordinates from a field. Thus, I do not see how commutivity of a field makes ax=xa true in general.
Thus, should algebra over a field be changed? Or is there some stricter form of algebra that includes this special property. Any help?
Thanks. -- TedPavlic 20:34, 21 February 2007 (UTC)
Hi Mct. I've seen you do a lot of good work in math articles. That's very appreciated. Thanks! Oleg Alexandrov ( talk) 00:56, 14 April 2007 (UTC)
I see you've pretty much written this article so I hope it's ok to ask you some stuff about it. Is the radical mentioned the same as Jacobson radical (there are a lot of equivalent formulations of the Jacobson radical but none on the page obviously matched what you had as the definition). If it is the same can we use that definition for general (not necessarily finite dimensional) algebras. If it isn't the Jacobson radical I think we need to disambiguate because semisimple algebra is definitely used in this sense in Banach algebra theory. Thanks. A Geek Tragedy 21:13, 25 May 2007 (UTC)
Hi, I came across this article which you wrote in March. My familiarity with Wold's decomposition is from signal processing, where it is stated as saying that any stochastic process can be represented as the sum of a deterministic process and a purely indeterministic process [1]. Is this a special case of your article? If so, do you think it would be worthwhile to write this special case as a section in the article, so that people (like me) who know nothing about operator theory could still make some sense of it? Cheers, Zvika 18:45, 17 June 2007 (UTC)
I still think it makes sense to have a section on the special case of stochastic processes, since right now the article is close to useless for people like me. Perhaps I will add this someday. A quick Google search seems to show that many (if not most) people interested in Wold decomposition really care about the stochastic process application. -- Zvika 12:16, 19 June 2007 (UTC)
Hello. I added this link because of the redirect " Eigendecomposition". Since the articles Spectral theorem and Eigendecomposition (matrix) are referring to that term, do you think that a disambiguation page would be a better option? Thanks, Korg ( talk) 22:38, 10 October 2007 (UTC)
When searching for help on commutative diagrams in Wikipedia, I found your question at: Wikipedia_talk:WikiProject_Mathematics/Archive_19#Commutative_diagram
I've figured out how to make them and documented it at: meta:Help:Displaying a formula#Commutative_diagrams; hope this helps!
Nbarth ( talk) 22:29, 25 November 2007 (UTC)
Thanks for your message! I am not totally satisfied with my edit of the proof though. When I have time, I'll change it slightly, concentrating from the beginning on the orthogonal of the kernel. This would fit better with the statement of the theorem, as it stands now. With best wishes, -- Bdmy ( talk) 17:58, 15 March 2009 (UTC)
Hi, in your edits for Spectrum (functional analysis) a couple of years ago, you changed the section on bounded operators to say that bijectivity is not required for invertibility (you suggested that the surjectivity requirement could be dropped in the edit text). I feel fairly confident that this is not correct; my understanding of the true situation is as follows (note: T is assumed to be linear, which implies all other maps mentioned below are):
It seems that you disagree with my point (2) above, but only in the bounded case. I think it is right for the following reasons:
It seems like this will have a knock on effect on lots of parts of this article at least one other ( Decomposition of spectrum (functional analysis)). I'd be particularly interested if you have a counterexample (a bounded operator with a bounded inverse which is not bijective). Quietbritishjim ( talk) 14:55, 20 June 2009 (UTC)
I am not sure why you reverted this edit: http://en.wikipedia.org/?title=Metric_tensor&diff=472976875&oldid=471471609. An inner product is positive-definite by definition; obviously, it is the metric tensor that needn't be positive-definite. Your suggestion to look at the definition was unenlightening. Thankfully the original statement has vanished from the article. — Preceding unsigned comment added by 220.245.107.17 ( talk) 07:19, 15 September 2012 (UTC)
This is just to let you know that I've replied to a message you left on the Fourier inversion theorem talk page a few months back. I've finished my proposed rewrite for that article so I also made a new section for that on the talk page. I assume the article's on your watchlist, but thought I'd leave a message here just to be safe. Thanks! Quietbritishjim ( talk) 01:42, 31 December 2012 (UTC)
I would like to understand the section you added in stationary process. I don't understand why any stationary process can be considered as a Fourier transform while the Bochner's theorem is only applied on the autocovariance function.
In fact, I posted this question here. If you could answer it, it would be a great help for me! Thanks! 木子溪 ( talk) 23:34, 7 December 2021 (UTC)
I can't hep but notice you are interested in them. You might find the current discussion here Talk:Many-worlds interpretation interesting.-- CSTAR 17:16, 15 May 2006 (UTC)
Why do you consider treating the heat bath as made up of a large number of loosely-couple copies of the main system is incorrect? (It enables you to then the results from the MCI for a large number of coupled discrete systems with a prescribed total energy.) Linuxlad 16:13, 19 May 2006 (UTC)
I apologize if my quick and harsh responses have felt like I was biting you, but deletion is a serious matter. However, I advise you to refrain from commenting on other editors' intelligence as you did, which is at the least uncivil and at worst a personal attack. In fact, I advise you to stop commenting so much in the AfD in general: you really haven't added anything new to the discussion since your nomination, and you should let the community speak. As you are a newcomer, though, let me direct you to Wikipedia:Introduction to Deletion Process, where you can learn about how deletion works and what the processes are, and where to read more, as well as Wikipedia:Moving and merging, where you can learn about how to deal with redundant or badly named articles. And if this is a question of not being sure you could edit out parts of an article by yourself, wikipedia encourages you to be bold. Mango juice talk 18:06, 22 May 2006 (UTC)
i thought the discussion was over as far as i was concerned, and i wasn't going to comment further. since you decide to come to my talk page i will respond, one last time. my question re your ability to read the article somewhat intelligently has become a question whether you can read it critically at all. in fact it has become obvious you're not competent to judge, from your comments. inability to recognice and distinguish relevant material is pretty clear. after initiating the process, i had assumed whatever objections encountered by the proposal would be well-informed and educated. whatever the deletion policy is, if all AfD's solicit such ignorant responses, hopefully not too many articles will go thru this nonsense in the future. Mct mht 18:26, 22 May 2006 (UTC)
i hope it's not inappropriate to have a comment such as this on the talk page. as can be seen above, i got into it a bit regarding an AfD. the full exchange is here. while that is over and done with, it seems to bring about questions regarding the deletion policy for articles of a particular nature.
my position was that the article derivation of the partition function is technically worthless. i assumed that whatever objections raised would be technically sound. when the justification of the first 2 votes to keep seemed to be superficial and had no apparent technical merit, i mentioned the question whether one is actually "required to read the article somewhat intelligently to enter the discussion" (my words), the responses of the two voters were:
1. one flat out stated that such requirement is unnecessary.
2. the second voter claimed to be insulted and offered further justifications/explanations which reinforced the suspicion that there's no real understanding behind his/her comments.
There is nothing uncivil about calling an ignorant comment what it is. it's unpleasant but it needs to be done. i am very happy, and did, listen to objections/suggestions raised that from those who understand the context, be they disagreements on the specific issues i raised or the overall value in retaining the article. it seems funny that a discussion on the deletion proposal for such an article would attract untrained attention, whose only interest, apparently, is to ensure that some "policy" is followed, as they understand that policy, sensibly or otherwise. the discussion then becomes pointless. as the risk of being overly dramatic, it would be similarly ridiculous to have an amateur sitting on the editorial board of, say, Phy. Lett. X (does it even go to X? :)), and decides what gets in the journal. again at the risk of overdramatizing, this reminds of the story when the physicist Alan Sokal, as a prank, submitted some gibberish to a sociology(?) journal and got accepted. it would be funny to see whether one can duplicate that here, write up some garbage filled with technical jargon, put it on AfD, and see whether it gets defended.
if that's the WP policy, so be it, but then one needs to be extra careful with actions which could bring un-knowledgable attention to articles, such as AfD. Mct mht 22:39, 22 May 2006 (UTC)
here you come again.
1. the vast majority of the technical articles on WP, certainly all the ones i've encountered, along with discussions on their talk pages, are very professional. certainly almost everyone on Wikipedia talk:WikiProject Mathematics seems to be a professional mathematician. that's why i was initially surprised the AfD attracted attention such as yours.
2. first you claim to possess adequate understanding and now say it's an obscure subject. as far as i am concerned, that renders your already zero credibility (in the present discussion) below zero. in any case, there's nothing obscure about statistical mechanics, millions of college kids know it, obscuredness is not relevant anyhow. don't excuse the ignorance.
3. i will leave the policy to the (self-appointed?) WP bureaucrats. however, as stated above, i will certainly be careful with actions that might attract undesirable interest.
hopefully this closes the discussion. and we can stay out of each other's way in the future. Mct mht 20:55, 24 May 2006 (UTC)
By the by, for future AfDs of physics articles, you can get some technical expertise in the dicussion by mentioning the AfD at Wikipedia talk:WikiProject Physics. That's how all the physicists found out about Wikipedia:Articles for deletion/Derivation of the partition function. — Laura Scudder ☎ 14:05, 25 May 2006 (UTC)
Greetings! Since you said the worthwhile information from Derivation of the partition function is present elsewhere in the encyclopedia, I infer that you know where it is. I don't, or I would do the following task: please change or remove the links broken by the deletion, which may be found here. (Only the links in actual article pages need fixing.) Ideally, the admin who did the deleting should have done this, but he may not have known to do so or may not have felt qualified to judge what changes should be made. -- Cyan 22:14, 17 June 2006 (UTC)
Thanks for this cleanup edit! [2]. -- HappyCamper 16:37, 16 August 2006 (UTC)
FYI: einstein's elevator vs. einstein's cabin. -- Jtir 17:03, 23 September 2006 (UTC)
FYI, I checked a couple of mathematical references and did not find the term. I don't know enough about the subject to have an opinion, but I did find the where functional analysis was added to the article. It was in there for three years! I find problems all the time in articles and not just technical ones. Sometimes it is helpful review the edit history to find out just when a problematic change was made. It might then be possible to contact the original editor and ask what he had in mind. If the editor was anonymous and left no edit summary, I feel comfortable removing the material. -- Jtir 19:04, 24 September 2006 (UTC)
would you mind taking it a little less personal? what's your problem? it is clear from your own talk page that you attack viciously anthing not to your liking. that might me fair. you also have to agree from time to time that you might have missed a detail and might also not be omnipotent. so i find it fair to ask wether you have other ways of response than labelling something general bs when you don't see all it includes. there is no point or reason in questioning your intelligence but you can slow down insulting mine. thank you. you can reply here, to my talk page or the quantum hamiltonian and i do expect some substance. thank you. andrej.westermann 04:06, 17 October 2006 (UTC)
This article is hopeless. Material gets added to this article that I have trouble even parsing. Can you make any sense out of the following graf?
-- CSTAR 17:26, 26 October 2006 (UTC)
Hello. On the 10 June 2006, you merged the article Pure state into Density matrix. The article at Pure state has since been recreated. Could you have another look at the article, and if necessary merge it again? Thanks. Mike Peel 10:39, 27 October 2006 (UTC)
Hi there, i apologise for the last-paragraph problem with the Enthalpy article, there's browser problems here which are causing textbox data loss mid-edit. I was wondering if you'd be interested in creating a collaboration project with regards to the Enthalpy article; there's a good basis of information, but it needs verifying and tone-changing.
I think it'd be nice to collaborate with a person of similar interests and expertise as myself. :-) JCraw 13:13, 27 November 2006 (UTC)
Mct mht, thank you for answering my questions on a variety of math talk pages. I've been learning a lot, and I think the process has improved the Wikipedia pages. Thanks. —Ben FrantzDale 11:26, 1 May 2007 (UTC)
Hi, I'm a little bit new to wikipedia so I'm not sure if this is the right way to contact you.
Although I'm on a different IP, I was the guy who edited the quantum teleportation article regarding the collapse of the qubits into a bell state. I trust that you know more about the subject than I do, but I wanted to point out that what I added was actually a direct quote from the article on bell states: http://en.wikipedia.org/wiki/Bell_state
So I just wanted to know, is the bell state article incorrect, or did I misinterpret it? 130.126.160.96 21:06, 2 May 2007 (UTC)
Note that because the qubits were not in a Bell state before, they get projected into a Bell state (according to the projection rule of quantum measurements), and as Bell states are entangled, a Bell measurement is an entangling operation.
Hello, I was a little puzzled by your edit summary in Hilbert space. If you believe that the sentence that you've removed should be replaced with a more accurate one, are you going to replace it yourself? I actually thought that the sentence was reasonable, and don't quite understand how (and mostly, why) are you going to project onto a non-closed subspace. For example, sequences with only finitely many non-zero terms are dense in l2 and form a linear subspace, but however you define the projection onto it, this projection will not have any good properties. Arcfrk 22:50, 3 May 2007 (UTC)
I am not sure I understand your comment about von Neumann algebras, but I agree that motivational section should provide good motivations, not massage technical details. Unfortunately, I can't find the right words to express the idea of algebraic vs topological consideration that you've alluded to. If you can overcome your laziness, it would be great if you fill in a sentence or two there. Arcfrk 04:22, 5 May 2007 (UTC)
The deleted article has been relisted at AfD: Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination). There you can express your opinion on whether to keep it or delete it. You should not just say keep or delete but also explain your rationale. Michael Hardy 18:24, 11 August 2007 (UTC)
Please note that i undid your undo, of a change that I made to the Triangular matrix article. The claim I removed is clearly false. As you sensibly recommended, I put a remark in the discussion page. Please do not revert the false section again. Tom Lougheed 01:25, 12 August 2007 (UTC)
Various properties of groups - amenability, a-T-menability, property (T) - are studied by geometric group theorists, ergodic theorists and operator algebraists alike. Each one can be defined by a geometric condition, as Gromov has pointed out. I am not so sure that these pages should automatically be classified as analysis, rather than geometry or topology. I think many geometric group theorists might take issue. The field of "algebra", however, for amenable groups was obviously wrong. This page by the way does not mention amenable actions, which I intend to add in the near future. The action on the Gromov boundary is amenable; it's hard to say whether that's geometry or analysis, because it's probably both. Mathsci 08:02, 29 September 2007 (UTC)
Hello -- After I added a brief section on the von Neumann equation to density matrix, you put in an edit note suggesting that it might be merged into mathematical formulation of quantum mechanics. I'm not sure exactly what you mean by this: If you mean that the section should be removed from the density matrix article, I would disagree -- it's certainly important information about the density matrix that belongs in an encyclopedia article about the density matrix, and in fact there's plenty in the "density matrix" article is also in the "math. formulation" article. If, on the other hand, you mean that there's content in one presentation but not the other that should be copied, it sounds like a great idea, although I'm not sure I'll get a chance to do so myself. Happy holidays! -- Steve ( talk) 06:32, 18 December 2007 (UTC)
Hi,
I notice that in May last year you removed the definition of the tensor product from the article on the tensor product of vector spaces. The edit summary indicates that you thought the definition was confusing; for this I apologize, as I gave that definition there, and perhaps I was less than clear. However, it was the only actual definition of the tensor product that the article contained! (which is why I took the time to add it! Yet this is typical of the shameful state of WP articles.) If you read the current version of the article carefully, you will notice that while it uses the otimes notation liberally, it never actually ever defines what otimes means, except by general dancing about and examples using finite algebra! Please consider restoring the deleted text, and/or modifying it so that otimes is actually defined. Thanks. linas ( talk) 04:12, 8 January 2008 (UTC)
Hi,
I saw some answers you replied at Talk:Quantum entanglement. I think you know pretty much about the quantum entanglement. Could you forgive me for making some discussion here?
I have studied a bit quantum mechanics because of my interest in the ability of parallelism of quantum computer. It seems that quantum entanglement plays a critical role to achieve the parallelism. I believe the entanglement phenomenon can be derived from the Schrödinger equation. The thought experiment of EPR paradox would be my evidence.
But after the study, I can not find an article which explains the relations between the Schrödinger equation and quantum entanglement so far. As below: (Part I: Quantum entanglement, Part II: Schrödinger equation and Part III: Question)
As I know, the entanglement only happens in composite system. For example, there are three systems , , (each of which consists of a single particle) with respective Hilbert space , , . The Hilbert space of composite system of the three is the tensor product of respective Hilbert spaces:
If each Hilbert space has two basis in the set:
and
If I am right, the composite Hilbert space will have basis (but not basis) in the set:
Therefore, is an 8-dimensional Hilbert space.
It means (again if I am right) any state of the composite system can be represent by an 8-dimensional vector.
Now, we try to described the composite system of three particles above by a 2-dimensional time-independent Schrödinger equation:
where , , , are position vectors.
The position vector of each particle is in the Cartesian coordinate (or Cartesian space). The composite wave function of the three is in the the space of cartesian product of respective Cartesian spaces:
where:
The composite space will have basis (but not basis) in the set:
Therefore, is a 6-dimensional Cartesian space. And .
1. My explanations in Part I & Part II look so similar to me. The wave function in Part II may be rewritten as does that mean the composite system in Part II can be written as a ket with six basis ?
2. Why the same composite system can have two explanations (Part I & Part II) but with different number of basis (8 versus 6)?
3. How to connect Schrödinger equation with quantum entanglement?
4. Why the entangled state is in the space yielded from tensor product rather than from cartesian product ?
-------- Justin545 ( talk) 10:04, 25 January 2008 (UTC)
FYI: A good resource on this topic is Preskill's lecture notes, if you haven't seen it before. -- Steve ( talk) 20:50, 27 January 2008 (UTC)
You removed the entire section of "Separable wave function and tensor product" in article "Separable states" at 01:43, 26 February 2008 (UTC). Could you give me the reasons? - Justin545 ( talk) 02:42, 26 February 2008 (UTC)
I made the change in order to explain why "definite" doesn't apply. Where am I in error? RandomTool2 ( talk) 23:46, 21 May 2008 (UTC)
Hi, you undid my recent edit of the Projective line, concerning its relationship to a topological circle. Hoping you can reply to my question on the discussion page. -- Cheers, Steelpillow 21:10, 27 May 2008 (UTC)
Hi again. I have modified my edit in the light of various recent discussions/comments, and because "finite" means different things in different contexts and I just realised that I had not made my usage clear. If you are still unhappy with it, please check out the Talk page before reverting again. Apologies for inviting comment in the edit summary, but you had not replied to my proposal and I didn't want to blank you. -- Cheers, Steelpillow 10:48, 7 June 2008 (UTC)
I wrote a comment on my talk page. Oleg Alexandrov ( talk) 03:08, 12 June 2008 (UTC)
Howdy, I undid a big deletion with no edit summary at Hermitian adjoint. I guess it was probably accidental. The deleted material wasn't shakespeare, but it was relevant and looked correct. If you did want to get rid of it, definitely include an edit summary, and for so much reasonable text maybe also on the talk page, so we know what's up. JackSchmidt ( talk) 03:04, 3 July 2008 (UTC)
you recently reverted my recent over at PD matrix. While in general it makes sense to include an edit summary, when you RV an registered user (especially one making a change discussed on the discussion page), I'd highly recommend you (a) write an edit summary and (b) write something in the discussion. Pdbailey ( talk) 04:03, 3 July 2008 (UTC)
Hi there, I noticed you deleted a bunch of stuff from the introduction of Quantum Teleportation. I'm neither a mathematician nor a physicist so I'm can't vouch for the validity of the information, however I understand enough to be the last person before you to try and make any sense of that page. The paragraph you deleted was the introduction before I added something more sensible. Could you add something to the Talk Page to explain that it was gibberish? Otherwise I fear whoever wrote it will just revert. Master z0b ( talk) 09:08, 17 July 2008 (UTC)
Please study the confusion at Talk:Homotopy, and comment there, if you have a better idea on how to make the text clearer!
As you can see, some users definitely have got the wrong idea that an homotopy equivalence would be an homotopy. Also view the confusing text in the section Homotopy#Homotopy equivalence and null-homotopy, from which you removed the {{ Contradict}}; this text shows that at least one editor has mixed up the concepts! The text
would make clear sense if "are homotopy equivalent" were replaced by "are homotopic"; but right now it looks rather confused.
(The fact that the two compositions of the equivalence and its "quasi-inverse" are homotopic to identites does not mean that an homotopy equivalence is some kind of homotopy. It isn't.)
Best regards, JoergenB ( talk) 20:56, 1 November 2008 (UTC)
I noticed that you weakened one of the statements in Eberlein–Šmulian theorem on the claim that there are infinite-dimensional normed spaces whose weak topology is metrizable. This is actually not true. The counterexample you gave was a separable Hilbert space. Although it is true that the weak topology is metrizable on norm-bounded subsets, it is not metrizable on the whole space. In fact, more generally the weak and weak-* topologies on a reflexive Banach space coincide, and it is easy to show using the Hahn-Banach theorem that a weak-* topology is never metrizable.
More generally the weak topology on a normed space X is not metrizable. Otherwise, by first countability there would be a sequence xn∗ in X∗ such that the weak neighborhoods
are a basis of neighborhoods at 0. But then for any fixed x∗∈X∗, the weak neighborhood must contain Wn for some n. It follows that x∗ is a linear combination of x1∗,...,xn∗. That is, the Banach space X* is a union of countably many finite-dimensional subspaces, in violation of the Baire category theorem. siℓℓy rabbit ( talk) 15:46, 16 December 2008 (UTC)
You recently deleted a note on SI units in the section of Stokes' theorem where Maxwell's equations are presented, with the comment that it is "absurd to imply a physical formula is valid only in certain units". Whether you like it or not, the differential forms presented are in fact for the electromagnetic fields expressed in SI units. In other systems of units, the differential forms as such look similar but may involve different scaling factors. For example, in Gaussian units, Faraday's law of induction takes the form , to be compared with the same law expressed in SI units, which yields . As a reference you may consult the standard textbook "Classical Electrodynamics" by J.D. Jackson, in which an entire chapter is devoted to the subject of Maxwell's equations expressed in different systems of units. Hakkasberra ( talk) 23:38, 10 January 2009 (UTC)
Why the revert on C*-algebras? It's more useful to mention that non-zero *-homomorphisms have norm 1 than to simply say they're non-expansive. And why not use the discussion page? 76.126.116.54 ( talk) 04:47, 16 March 2009 (UTC)
Hi, Mct mht. I saw that you wrote most of the article on Choi's_theorem_on_completely_positive_maps, which current is the destination for a redirect if anyone searches for "completely positive map". I was thinking it would be more logical to move the contents of the page to "Completely Positive Map" with a large section on Choi's theorem (or, if the page got to large in the future, I would move the material on Choi's theorem to its own page, separate from the CPM page).
Do you feel strongly about this?
Thanks Njerseyguy ( talk) 19:08, 17 May 2010 (UTC)
I've no idea what it is. Could you provide a definition and a reference? See Talk:Cauchy–Schwarz inequality#No definition of 2-positivity in the article & [3]. Regards, Qwfp ( talk) 18:54, 25 October 2010 (UTC)
You are more than welcome to continue making quality contributions to Wikipedia. Note that because you are a logged-in user, you can create articles yourself, and don't have to post a request. However, you are more than welcome to continue submitting work to Articles for Creation.
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13:51, 23 November 2015 (UTC)
First, thanks for your work on the article on quantum relative entropy. My comment relates to the divergence property of S(ρ||σ) in the subsection Non-finite relative entropy. The demonstration of the divergence of the relative entropy diverges is a good one I think. However, only positive comments follow (i.e. "This makes physical sense. Informally, ..."). The negative repercussions of the divergence are not mentioned. Specifically, S(ρ||σ) can diverge when ρ and σ differ by an epsilon amount (as measured by some norm). An example: let σ have the diagonal representation with for and for , and let for a small positive number . As ρ has support (i.e. ) in the null space of σ, S(ρ||σ) is divergent even though the trace norm of the difference ρ-σ is 2ε. I think this should be pointed out as a negative feature of the relative entropy. What's your take on this? DireNeed ( talk) 06:54, 8 April 2017 (UTC)
Mct mht ("This is my haus, nigga, my haus!" -Yao Ming to Rasho Nesterović ) 14:12, 26 August 2006 (UTC)
I am also 24.155.72.152 (talk) on a few of the math pages. Mct mht 01:50, 5 April 2006 (UTC)
Welcome!
Hello, Mct mht, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:
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Oleg Alexandrov (
talk)
23:16, 2 April 2006 (UTC)
You are removing the assumption that some measurable functions have real values from a lot of places. But then you can't talk about almost everywhere convergence, you need values at least in a metric space.
Do you have references when those theorems hold? I suggeest you go back to the real number-valued functions, and that's the classical case, and it is surely correct. Thanks, and you can reply here. Oleg Alexandrov ( talk) 15:10, 12 April 2006 (UTC)
Yeah, in fact it is kind of weird that the previous contributors imposed the real-valued assumption. Surely something like the dominated convergence theorem, Egorov's, and Lusin's don't need that assumption. Should be in any reasonably modern introductory text on real analysis. Mct mht 19:22, 12 April 2006 (UTC)
A side note, apparently there are Lusin type results for Bochner integrals. Didn't know that. Mct mht
Hi. It seems you're still working on square root of a matrix, so I won't edit that page myself at the moment. However, could you please bear in mind that the phrase "positive matrix" is often used to describe a matrix with positive entries? I gather that you're talking about a positive-definite matrix. Great work, by the way. Cheers, Jitse Niesen ( talk) 10:01, 17 August 2006 (UTC)
Hi,
Back in August, you removed some text from resolvent formalism, and I don't understand why. Could you take a look at the talk page? linas 03:49, 27 October 2006 (UTC)
Hello. You reversed a change I made to vector space. Part of the reason why I was confident about that change was because the algebra over a field article states that the bilinear multiplication operator must be such that (ax)(by)=(ab)(x y). However, now that I look into the formal definition of bilinear, I do not see how this follows. That being said, I think that there are many important results (for example, results about commutable operators and their eigenspaces) that depend on this. It seems like there should be some stronger version of algebra that includes this property. I understand that in most cases this is a result of the commutivity of the field; however, strictly speaking the commutivity of the field should have nothing to do with ax=xa. Right? That is, a vector x need not have coordinates from the field. All I need with an algebra is some definition of scalar-vector multiplication; I can do that without having vector coordinates from a field. Thus, I do not see how commutivity of a field makes ax=xa true in general.
Thus, should algebra over a field be changed? Or is there some stricter form of algebra that includes this special property. Any help?
Thanks. -- TedPavlic 20:34, 21 February 2007 (UTC)
Hi Mct. I've seen you do a lot of good work in math articles. That's very appreciated. Thanks! Oleg Alexandrov ( talk) 00:56, 14 April 2007 (UTC)
I see you've pretty much written this article so I hope it's ok to ask you some stuff about it. Is the radical mentioned the same as Jacobson radical (there are a lot of equivalent formulations of the Jacobson radical but none on the page obviously matched what you had as the definition). If it is the same can we use that definition for general (not necessarily finite dimensional) algebras. If it isn't the Jacobson radical I think we need to disambiguate because semisimple algebra is definitely used in this sense in Banach algebra theory. Thanks. A Geek Tragedy 21:13, 25 May 2007 (UTC)
Hi, I came across this article which you wrote in March. My familiarity with Wold's decomposition is from signal processing, where it is stated as saying that any stochastic process can be represented as the sum of a deterministic process and a purely indeterministic process [1]. Is this a special case of your article? If so, do you think it would be worthwhile to write this special case as a section in the article, so that people (like me) who know nothing about operator theory could still make some sense of it? Cheers, Zvika 18:45, 17 June 2007 (UTC)
I still think it makes sense to have a section on the special case of stochastic processes, since right now the article is close to useless for people like me. Perhaps I will add this someday. A quick Google search seems to show that many (if not most) people interested in Wold decomposition really care about the stochastic process application. -- Zvika 12:16, 19 June 2007 (UTC)
Hello. I added this link because of the redirect " Eigendecomposition". Since the articles Spectral theorem and Eigendecomposition (matrix) are referring to that term, do you think that a disambiguation page would be a better option? Thanks, Korg ( talk) 22:38, 10 October 2007 (UTC)
When searching for help on commutative diagrams in Wikipedia, I found your question at: Wikipedia_talk:WikiProject_Mathematics/Archive_19#Commutative_diagram
I've figured out how to make them and documented it at: meta:Help:Displaying a formula#Commutative_diagrams; hope this helps!
Nbarth ( talk) 22:29, 25 November 2007 (UTC)
Thanks for your message! I am not totally satisfied with my edit of the proof though. When I have time, I'll change it slightly, concentrating from the beginning on the orthogonal of the kernel. This would fit better with the statement of the theorem, as it stands now. With best wishes, -- Bdmy ( talk) 17:58, 15 March 2009 (UTC)
Hi, in your edits for Spectrum (functional analysis) a couple of years ago, you changed the section on bounded operators to say that bijectivity is not required for invertibility (you suggested that the surjectivity requirement could be dropped in the edit text). I feel fairly confident that this is not correct; my understanding of the true situation is as follows (note: T is assumed to be linear, which implies all other maps mentioned below are):
It seems that you disagree with my point (2) above, but only in the bounded case. I think it is right for the following reasons:
It seems like this will have a knock on effect on lots of parts of this article at least one other ( Decomposition of spectrum (functional analysis)). I'd be particularly interested if you have a counterexample (a bounded operator with a bounded inverse which is not bijective). Quietbritishjim ( talk) 14:55, 20 June 2009 (UTC)
I am not sure why you reverted this edit: http://en.wikipedia.org/?title=Metric_tensor&diff=472976875&oldid=471471609. An inner product is positive-definite by definition; obviously, it is the metric tensor that needn't be positive-definite. Your suggestion to look at the definition was unenlightening. Thankfully the original statement has vanished from the article. — Preceding unsigned comment added by 220.245.107.17 ( talk) 07:19, 15 September 2012 (UTC)
This is just to let you know that I've replied to a message you left on the Fourier inversion theorem talk page a few months back. I've finished my proposed rewrite for that article so I also made a new section for that on the talk page. I assume the article's on your watchlist, but thought I'd leave a message here just to be safe. Thanks! Quietbritishjim ( talk) 01:42, 31 December 2012 (UTC)
I would like to understand the section you added in stationary process. I don't understand why any stationary process can be considered as a Fourier transform while the Bochner's theorem is only applied on the autocovariance function.
In fact, I posted this question here. If you could answer it, it would be a great help for me! Thanks! 木子溪 ( talk) 23:34, 7 December 2021 (UTC)
I can't hep but notice you are interested in them. You might find the current discussion here Talk:Many-worlds interpretation interesting.-- CSTAR 17:16, 15 May 2006 (UTC)
Why do you consider treating the heat bath as made up of a large number of loosely-couple copies of the main system is incorrect? (It enables you to then the results from the MCI for a large number of coupled discrete systems with a prescribed total energy.) Linuxlad 16:13, 19 May 2006 (UTC)
I apologize if my quick and harsh responses have felt like I was biting you, but deletion is a serious matter. However, I advise you to refrain from commenting on other editors' intelligence as you did, which is at the least uncivil and at worst a personal attack. In fact, I advise you to stop commenting so much in the AfD in general: you really haven't added anything new to the discussion since your nomination, and you should let the community speak. As you are a newcomer, though, let me direct you to Wikipedia:Introduction to Deletion Process, where you can learn about how deletion works and what the processes are, and where to read more, as well as Wikipedia:Moving and merging, where you can learn about how to deal with redundant or badly named articles. And if this is a question of not being sure you could edit out parts of an article by yourself, wikipedia encourages you to be bold. Mango juice talk 18:06, 22 May 2006 (UTC)
i thought the discussion was over as far as i was concerned, and i wasn't going to comment further. since you decide to come to my talk page i will respond, one last time. my question re your ability to read the article somewhat intelligently has become a question whether you can read it critically at all. in fact it has become obvious you're not competent to judge, from your comments. inability to recognice and distinguish relevant material is pretty clear. after initiating the process, i had assumed whatever objections encountered by the proposal would be well-informed and educated. whatever the deletion policy is, if all AfD's solicit such ignorant responses, hopefully not too many articles will go thru this nonsense in the future. Mct mht 18:26, 22 May 2006 (UTC)
i hope it's not inappropriate to have a comment such as this on the talk page. as can be seen above, i got into it a bit regarding an AfD. the full exchange is here. while that is over and done with, it seems to bring about questions regarding the deletion policy for articles of a particular nature.
my position was that the article derivation of the partition function is technically worthless. i assumed that whatever objections raised would be technically sound. when the justification of the first 2 votes to keep seemed to be superficial and had no apparent technical merit, i mentioned the question whether one is actually "required to read the article somewhat intelligently to enter the discussion" (my words), the responses of the two voters were:
1. one flat out stated that such requirement is unnecessary.
2. the second voter claimed to be insulted and offered further justifications/explanations which reinforced the suspicion that there's no real understanding behind his/her comments.
There is nothing uncivil about calling an ignorant comment what it is. it's unpleasant but it needs to be done. i am very happy, and did, listen to objections/suggestions raised that from those who understand the context, be they disagreements on the specific issues i raised or the overall value in retaining the article. it seems funny that a discussion on the deletion proposal for such an article would attract untrained attention, whose only interest, apparently, is to ensure that some "policy" is followed, as they understand that policy, sensibly or otherwise. the discussion then becomes pointless. as the risk of being overly dramatic, it would be similarly ridiculous to have an amateur sitting on the editorial board of, say, Phy. Lett. X (does it even go to X? :)), and decides what gets in the journal. again at the risk of overdramatizing, this reminds of the story when the physicist Alan Sokal, as a prank, submitted some gibberish to a sociology(?) journal and got accepted. it would be funny to see whether one can duplicate that here, write up some garbage filled with technical jargon, put it on AfD, and see whether it gets defended.
if that's the WP policy, so be it, but then one needs to be extra careful with actions which could bring un-knowledgable attention to articles, such as AfD. Mct mht 22:39, 22 May 2006 (UTC)
here you come again.
1. the vast majority of the technical articles on WP, certainly all the ones i've encountered, along with discussions on their talk pages, are very professional. certainly almost everyone on Wikipedia talk:WikiProject Mathematics seems to be a professional mathematician. that's why i was initially surprised the AfD attracted attention such as yours.
2. first you claim to possess adequate understanding and now say it's an obscure subject. as far as i am concerned, that renders your already zero credibility (in the present discussion) below zero. in any case, there's nothing obscure about statistical mechanics, millions of college kids know it, obscuredness is not relevant anyhow. don't excuse the ignorance.
3. i will leave the policy to the (self-appointed?) WP bureaucrats. however, as stated above, i will certainly be careful with actions that might attract undesirable interest.
hopefully this closes the discussion. and we can stay out of each other's way in the future. Mct mht 20:55, 24 May 2006 (UTC)
By the by, for future AfDs of physics articles, you can get some technical expertise in the dicussion by mentioning the AfD at Wikipedia talk:WikiProject Physics. That's how all the physicists found out about Wikipedia:Articles for deletion/Derivation of the partition function. — Laura Scudder ☎ 14:05, 25 May 2006 (UTC)
Greetings! Since you said the worthwhile information from Derivation of the partition function is present elsewhere in the encyclopedia, I infer that you know where it is. I don't, or I would do the following task: please change or remove the links broken by the deletion, which may be found here. (Only the links in actual article pages need fixing.) Ideally, the admin who did the deleting should have done this, but he may not have known to do so or may not have felt qualified to judge what changes should be made. -- Cyan 22:14, 17 June 2006 (UTC)
Thanks for this cleanup edit! [2]. -- HappyCamper 16:37, 16 August 2006 (UTC)
FYI: einstein's elevator vs. einstein's cabin. -- Jtir 17:03, 23 September 2006 (UTC)
FYI, I checked a couple of mathematical references and did not find the term. I don't know enough about the subject to have an opinion, but I did find the where functional analysis was added to the article. It was in there for three years! I find problems all the time in articles and not just technical ones. Sometimes it is helpful review the edit history to find out just when a problematic change was made. It might then be possible to contact the original editor and ask what he had in mind. If the editor was anonymous and left no edit summary, I feel comfortable removing the material. -- Jtir 19:04, 24 September 2006 (UTC)
would you mind taking it a little less personal? what's your problem? it is clear from your own talk page that you attack viciously anthing not to your liking. that might me fair. you also have to agree from time to time that you might have missed a detail and might also not be omnipotent. so i find it fair to ask wether you have other ways of response than labelling something general bs when you don't see all it includes. there is no point or reason in questioning your intelligence but you can slow down insulting mine. thank you. you can reply here, to my talk page or the quantum hamiltonian and i do expect some substance. thank you. andrej.westermann 04:06, 17 October 2006 (UTC)
This article is hopeless. Material gets added to this article that I have trouble even parsing. Can you make any sense out of the following graf?
-- CSTAR 17:26, 26 October 2006 (UTC)
Hello. On the 10 June 2006, you merged the article Pure state into Density matrix. The article at Pure state has since been recreated. Could you have another look at the article, and if necessary merge it again? Thanks. Mike Peel 10:39, 27 October 2006 (UTC)
Hi there, i apologise for the last-paragraph problem with the Enthalpy article, there's browser problems here which are causing textbox data loss mid-edit. I was wondering if you'd be interested in creating a collaboration project with regards to the Enthalpy article; there's a good basis of information, but it needs verifying and tone-changing.
I think it'd be nice to collaborate with a person of similar interests and expertise as myself. :-) JCraw 13:13, 27 November 2006 (UTC)
Mct mht, thank you for answering my questions on a variety of math talk pages. I've been learning a lot, and I think the process has improved the Wikipedia pages. Thanks. —Ben FrantzDale 11:26, 1 May 2007 (UTC)
Hi, I'm a little bit new to wikipedia so I'm not sure if this is the right way to contact you.
Although I'm on a different IP, I was the guy who edited the quantum teleportation article regarding the collapse of the qubits into a bell state. I trust that you know more about the subject than I do, but I wanted to point out that what I added was actually a direct quote from the article on bell states: http://en.wikipedia.org/wiki/Bell_state
So I just wanted to know, is the bell state article incorrect, or did I misinterpret it? 130.126.160.96 21:06, 2 May 2007 (UTC)
Note that because the qubits were not in a Bell state before, they get projected into a Bell state (according to the projection rule of quantum measurements), and as Bell states are entangled, a Bell measurement is an entangling operation.
Hello, I was a little puzzled by your edit summary in Hilbert space. If you believe that the sentence that you've removed should be replaced with a more accurate one, are you going to replace it yourself? I actually thought that the sentence was reasonable, and don't quite understand how (and mostly, why) are you going to project onto a non-closed subspace. For example, sequences with only finitely many non-zero terms are dense in l2 and form a linear subspace, but however you define the projection onto it, this projection will not have any good properties. Arcfrk 22:50, 3 May 2007 (UTC)
I am not sure I understand your comment about von Neumann algebras, but I agree that motivational section should provide good motivations, not massage technical details. Unfortunately, I can't find the right words to express the idea of algebraic vs topological consideration that you've alluded to. If you can overcome your laziness, it would be great if you fill in a sentence or two there. Arcfrk 04:22, 5 May 2007 (UTC)
The deleted article has been relisted at AfD: Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination). There you can express your opinion on whether to keep it or delete it. You should not just say keep or delete but also explain your rationale. Michael Hardy 18:24, 11 August 2007 (UTC)
Please note that i undid your undo, of a change that I made to the Triangular matrix article. The claim I removed is clearly false. As you sensibly recommended, I put a remark in the discussion page. Please do not revert the false section again. Tom Lougheed 01:25, 12 August 2007 (UTC)
Various properties of groups - amenability, a-T-menability, property (T) - are studied by geometric group theorists, ergodic theorists and operator algebraists alike. Each one can be defined by a geometric condition, as Gromov has pointed out. I am not so sure that these pages should automatically be classified as analysis, rather than geometry or topology. I think many geometric group theorists might take issue. The field of "algebra", however, for amenable groups was obviously wrong. This page by the way does not mention amenable actions, which I intend to add in the near future. The action on the Gromov boundary is amenable; it's hard to say whether that's geometry or analysis, because it's probably both. Mathsci 08:02, 29 September 2007 (UTC)
Hello -- After I added a brief section on the von Neumann equation to density matrix, you put in an edit note suggesting that it might be merged into mathematical formulation of quantum mechanics. I'm not sure exactly what you mean by this: If you mean that the section should be removed from the density matrix article, I would disagree -- it's certainly important information about the density matrix that belongs in an encyclopedia article about the density matrix, and in fact there's plenty in the "density matrix" article is also in the "math. formulation" article. If, on the other hand, you mean that there's content in one presentation but not the other that should be copied, it sounds like a great idea, although I'm not sure I'll get a chance to do so myself. Happy holidays! -- Steve ( talk) 06:32, 18 December 2007 (UTC)
Hi,
I notice that in May last year you removed the definition of the tensor product from the article on the tensor product of vector spaces. The edit summary indicates that you thought the definition was confusing; for this I apologize, as I gave that definition there, and perhaps I was less than clear. However, it was the only actual definition of the tensor product that the article contained! (which is why I took the time to add it! Yet this is typical of the shameful state of WP articles.) If you read the current version of the article carefully, you will notice that while it uses the otimes notation liberally, it never actually ever defines what otimes means, except by general dancing about and examples using finite algebra! Please consider restoring the deleted text, and/or modifying it so that otimes is actually defined. Thanks. linas ( talk) 04:12, 8 January 2008 (UTC)
Hi,
I saw some answers you replied at Talk:Quantum entanglement. I think you know pretty much about the quantum entanglement. Could you forgive me for making some discussion here?
I have studied a bit quantum mechanics because of my interest in the ability of parallelism of quantum computer. It seems that quantum entanglement plays a critical role to achieve the parallelism. I believe the entanglement phenomenon can be derived from the Schrödinger equation. The thought experiment of EPR paradox would be my evidence.
But after the study, I can not find an article which explains the relations between the Schrödinger equation and quantum entanglement so far. As below: (Part I: Quantum entanglement, Part II: Schrödinger equation and Part III: Question)
As I know, the entanglement only happens in composite system. For example, there are three systems , , (each of which consists of a single particle) with respective Hilbert space , , . The Hilbert space of composite system of the three is the tensor product of respective Hilbert spaces:
If each Hilbert space has two basis in the set:
and
If I am right, the composite Hilbert space will have basis (but not basis) in the set:
Therefore, is an 8-dimensional Hilbert space.
It means (again if I am right) any state of the composite system can be represent by an 8-dimensional vector.
Now, we try to described the composite system of three particles above by a 2-dimensional time-independent Schrödinger equation:
where , , , are position vectors.
The position vector of each particle is in the Cartesian coordinate (or Cartesian space). The composite wave function of the three is in the the space of cartesian product of respective Cartesian spaces:
where:
The composite space will have basis (but not basis) in the set:
Therefore, is a 6-dimensional Cartesian space. And .
1. My explanations in Part I & Part II look so similar to me. The wave function in Part II may be rewritten as does that mean the composite system in Part II can be written as a ket with six basis ?
2. Why the same composite system can have two explanations (Part I & Part II) but with different number of basis (8 versus 6)?
3. How to connect Schrödinger equation with quantum entanglement?
4. Why the entangled state is in the space yielded from tensor product rather than from cartesian product ?
-------- Justin545 ( talk) 10:04, 25 January 2008 (UTC)
FYI: A good resource on this topic is Preskill's lecture notes, if you haven't seen it before. -- Steve ( talk) 20:50, 27 January 2008 (UTC)
You removed the entire section of "Separable wave function and tensor product" in article "Separable states" at 01:43, 26 February 2008 (UTC). Could you give me the reasons? - Justin545 ( talk) 02:42, 26 February 2008 (UTC)
I made the change in order to explain why "definite" doesn't apply. Where am I in error? RandomTool2 ( talk) 23:46, 21 May 2008 (UTC)
Hi, you undid my recent edit of the Projective line, concerning its relationship to a topological circle. Hoping you can reply to my question on the discussion page. -- Cheers, Steelpillow 21:10, 27 May 2008 (UTC)
Hi again. I have modified my edit in the light of various recent discussions/comments, and because "finite" means different things in different contexts and I just realised that I had not made my usage clear. If you are still unhappy with it, please check out the Talk page before reverting again. Apologies for inviting comment in the edit summary, but you had not replied to my proposal and I didn't want to blank you. -- Cheers, Steelpillow 10:48, 7 June 2008 (UTC)
I wrote a comment on my talk page. Oleg Alexandrov ( talk) 03:08, 12 June 2008 (UTC)
Howdy, I undid a big deletion with no edit summary at Hermitian adjoint. I guess it was probably accidental. The deleted material wasn't shakespeare, but it was relevant and looked correct. If you did want to get rid of it, definitely include an edit summary, and for so much reasonable text maybe also on the talk page, so we know what's up. JackSchmidt ( talk) 03:04, 3 July 2008 (UTC)
you recently reverted my recent over at PD matrix. While in general it makes sense to include an edit summary, when you RV an registered user (especially one making a change discussed on the discussion page), I'd highly recommend you (a) write an edit summary and (b) write something in the discussion. Pdbailey ( talk) 04:03, 3 July 2008 (UTC)
Hi there, I noticed you deleted a bunch of stuff from the introduction of Quantum Teleportation. I'm neither a mathematician nor a physicist so I'm can't vouch for the validity of the information, however I understand enough to be the last person before you to try and make any sense of that page. The paragraph you deleted was the introduction before I added something more sensible. Could you add something to the Talk Page to explain that it was gibberish? Otherwise I fear whoever wrote it will just revert. Master z0b ( talk) 09:08, 17 July 2008 (UTC)
Please study the confusion at Talk:Homotopy, and comment there, if you have a better idea on how to make the text clearer!
As you can see, some users definitely have got the wrong idea that an homotopy equivalence would be an homotopy. Also view the confusing text in the section Homotopy#Homotopy equivalence and null-homotopy, from which you removed the {{ Contradict}}; this text shows that at least one editor has mixed up the concepts! The text
would make clear sense if "are homotopy equivalent" were replaced by "are homotopic"; but right now it looks rather confused.
(The fact that the two compositions of the equivalence and its "quasi-inverse" are homotopic to identites does not mean that an homotopy equivalence is some kind of homotopy. It isn't.)
Best regards, JoergenB ( talk) 20:56, 1 November 2008 (UTC)
I noticed that you weakened one of the statements in Eberlein–Šmulian theorem on the claim that there are infinite-dimensional normed spaces whose weak topology is metrizable. This is actually not true. The counterexample you gave was a separable Hilbert space. Although it is true that the weak topology is metrizable on norm-bounded subsets, it is not metrizable on the whole space. In fact, more generally the weak and weak-* topologies on a reflexive Banach space coincide, and it is easy to show using the Hahn-Banach theorem that a weak-* topology is never metrizable.
More generally the weak topology on a normed space X is not metrizable. Otherwise, by first countability there would be a sequence xn∗ in X∗ such that the weak neighborhoods
are a basis of neighborhoods at 0. But then for any fixed x∗∈X∗, the weak neighborhood must contain Wn for some n. It follows that x∗ is a linear combination of x1∗,...,xn∗. That is, the Banach space X* is a union of countably many finite-dimensional subspaces, in violation of the Baire category theorem. siℓℓy rabbit ( talk) 15:46, 16 December 2008 (UTC)
You recently deleted a note on SI units in the section of Stokes' theorem where Maxwell's equations are presented, with the comment that it is "absurd to imply a physical formula is valid only in certain units". Whether you like it or not, the differential forms presented are in fact for the electromagnetic fields expressed in SI units. In other systems of units, the differential forms as such look similar but may involve different scaling factors. For example, in Gaussian units, Faraday's law of induction takes the form , to be compared with the same law expressed in SI units, which yields . As a reference you may consult the standard textbook "Classical Electrodynamics" by J.D. Jackson, in which an entire chapter is devoted to the subject of Maxwell's equations expressed in different systems of units. Hakkasberra ( talk) 23:38, 10 January 2009 (UTC)
Why the revert on C*-algebras? It's more useful to mention that non-zero *-homomorphisms have norm 1 than to simply say they're non-expansive. And why not use the discussion page? 76.126.116.54 ( talk) 04:47, 16 March 2009 (UTC)
Hi, Mct mht. I saw that you wrote most of the article on Choi's_theorem_on_completely_positive_maps, which current is the destination for a redirect if anyone searches for "completely positive map". I was thinking it would be more logical to move the contents of the page to "Completely Positive Map" with a large section on Choi's theorem (or, if the page got to large in the future, I would move the material on Choi's theorem to its own page, separate from the CPM page).
Do you feel strongly about this?
Thanks Njerseyguy ( talk) 19:08, 17 May 2010 (UTC)
I've no idea what it is. Could you provide a definition and a reference? See Talk:Cauchy–Schwarz inequality#No definition of 2-positivity in the article & [3]. Regards, Qwfp ( talk) 18:54, 25 October 2010 (UTC)
You are more than welcome to continue making quality contributions to Wikipedia. Note that because you are a logged-in user, you can create articles yourself, and don't have to post a request. However, you are more than welcome to continue submitting work to Articles for Creation.
Thank you for helping improve Wikipedia!
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First, thanks for your work on the article on quantum relative entropy. My comment relates to the divergence property of S(ρ||σ) in the subsection Non-finite relative entropy. The demonstration of the divergence of the relative entropy diverges is a good one I think. However, only positive comments follow (i.e. "This makes physical sense. Informally, ..."). The negative repercussions of the divergence are not mentioned. Specifically, S(ρ||σ) can diverge when ρ and σ differ by an epsilon amount (as measured by some norm). An example: let σ have the diagonal representation with for and for , and let for a small positive number . As ρ has support (i.e. ) in the null space of σ, S(ρ||σ) is divergent even though the trace norm of the difference ρ-σ is 2ε. I think this should be pointed out as a negative feature of the relative entropy. What's your take on this? DireNeed ( talk) 06:54, 8 April 2017 (UTC)