Hi!
I anwsered to you on Talk:Cupola_(geometry)!
See you later! Padex ( talk) 17:21, 7 August 2009 (UTC)
Yes, the introduction seems to be an improvement. I'm still not entirely sure I know what it is, but I'm less unclear about how unclear I am now. ;-)- ( User) Wolfkeeper ( Talk) 03:20, 4 September 2009 (UTC)
I love the IPA and use it. The issue is its appropriate use in appropriate contexts.
So I must not ignore other editors, but they may ignore me. How does that work?
By the way, the correct idiom is "free rein," not "free reign." Wahrmund ( talk) 23:10, 10 November 2009 (UTC)
"and the distinction of <v> from <f> for medio-final /v/ to become merely etymological."
What do you mean? That the distinction is only made in the spelling and no longer in the language? Also, there was a medial distinction between /f/ and /v/ ('sævar' vs. 'sofa') but there wasn't any final distinction, was there? Haukur ( talk) 23:51, 28 November 2009 (UTC)
Thanks! Briangotts (Talk) (Contrib) 14:51, 30 November 2009 (UTC)
Hello. In case you didn't know, when you add content to talk pages and Wikipedia pages that have open discussion, you should sign your posts by typing four tildes ( ~~~~ ) at the end of your comment. You may also click on the signature button located above the edit window. This will automatically insert a signature with your username or IP address and the time you posted the comment. This information is useful because other editors will be able to tell who said what, and when. Thank you. -- SineBot ( talk) 09:04, 1 December 2009 (UTC)
I didn't remove any references, I merely moved the speculation about Þorodd out of the first paragraph of the article... AnonMoos ( talk) 03:56, 27 December 2009 (UTC)
See Talk:First Grammatical Treatise. AnonMoos ( talk) 23:57, 28 December 2009 (UTC)
Please refer to WP:MOSMATH. Periods go inside the math tags. Sławomir Biały ( talk) 02:07, 31 December 2009 (UTC)
Huh? Sorry, but those comments are old, and I'm really not sure which comment you´re referring to. But I cannot see any claim from me that dansk tunga wasn't used about the Danish language as it was spoken then. Icelandic court documents from the 10th century referred to dansk tunga and Snorrí also used the term dansk tunga. I'm perfectly aware that the language spoken in the north-germanic areas was called danish by it's speakers (tongue being synomym to language as in Icelandic tungumál, Danish tungemål). As far as I can see I'm only discussing the correct use of danish tongue and whether it can be used about Old Norwegian and Old Icelandic if the term Old Norse only refers to those dialects. Of course you may think of a completely different comment, in which case my reply is pure nonsense ;) Dylansmrjones ( talk) 21:45, 2 February 2010 (UTC)
The Original Barnstar | ||
I award LokiClock this barnstar for his enthusiastic contributions to articles on the Old Norse language. Haukur ( talk) 20:24, 7 February 2010 (UTC) |
Please don't add {{ stub}} tags to articles such as Málaháttr when they already have a subject-specific stub tag. And when you're adding stub tags, please put them at the end, as per WP:LAYOUT, not at the start. Thanks. PamD ( talk) 22:11, 21 April 2010 (UTC)
This is a courtesy note to let you know that the C++0x#Criticisms section you added is still empty, and that the discussion on the talk page may result in it being deleted on Jun 18 2010, if there is no sourced content in it at that time. -- Sacolcor ( talk) 15:28, 4 June 2010 (UTC)
Part of a series on |
Old Norse |
---|
WikiProject Norse history and culture |
G'day, I've noticed that you're quite active on Old Norse articles, so I thought you might be interested in this template. Feel free to add, remove, or rearrange things. Hayden120 ( talk) 05:31, 17 June 2010 (UTC)
I have added the "reviewers" property to your user account. This property is related to the Pending changes system that is currently being tried. This system loosens page protection by allowing anonymous users to make "pending" changes which don't become "live" until they're "reviewed". However, logged-in users always see the very latest version of each page with no delay. A good explanation of the system is given in this image. The system is only being used for pages that would otherwise be protected from editing.
If there are "pending" (unreviewed) edits for a page, they will be apparent in a page's history screen; you do not have to go looking for them. There is, however, a list of all articles with changes awaiting review at Special:OldReviewedPages. Because there are so few pages in the trial so far, the latter list is almost always empty. The list of all pages in the pending review system is at Special:StablePages.
To use the system, you can simply edit the page as you normally would, but you should also mark the latest revision as "reviewed" if you have looked at it to ensure it isn't problematic. Edits should generally be accepted if you wouldn't undo them in normal editing: they don't have obvious vandalism, personal attacks, etc. If an edit is problematic, you can fix it by editing or undoing it, just like normal. You are permitted to mark your own changes as reviewed.
The "reviewers" property does not obligate you to do any additional work, and if you like you can simply ignore it. The expectation is that many users will have this property, so that they can review pending revisions in the course of normal editing. However, if you explicitly want to decline the "reviewer" property, you may ask any administrator to remove it for you at any time. — Carl ( CBM · talk) 12:33, 18 June 2010 (UTC) — Carl ( CBM · talk) 13:29, 18 June 2010 (UTC)
Why did you revert my addition of <ǿ> to the transcription list? My authority for stating that this is a modern, scholarly way of representing /ø:/ in Old Norse is Terje Spurkland: "Innføring i norrønt språk", Universitetsforlaget, 9th edition (2007). This is the standard textbook in Old Norse at the University of Oslo. From a typographical point of view, I too prefer <œ>, but that doesn't change the fact. Devanatha ( talk) 16:31, 6 July 2010 (UTC)
IMO Putting Wylie and IPA together like this tends to confuse the difference between a transliteration system (Wylie) and a transcription (IPA) system. The IPA transcription of the sounds of the isolated Tibetan consonants more properly belongs in the article on the Tibetan script ~ perhaps we should insert the IPA transcriptions there and provide a link?. In his original article on the system Turrell V. Wylie did not detail the sounds of the letters - though he did mistakenly call the system he outlined Tibetan transcription. Can we just put the IPA in the article on Tibetan script and then remove it in the Wylie transliteration article? Chris Fynn ( talk) 10:11, 29 August 2010 (UTC)
Why did you remove this table from Old Norse orthography? Although the orthography of Old Norse was not completely consistent, the table still gave a general idea of the consonants and the Latin graphemes that were used to represent them. This is not covered anywhere else in the article – only vowels are covered. Thanks, Hayden120 ( talk) 06:15, 18 October 2010 (UTC)
I responded on my talk page. Benwing ( talk) 10:16, 17 May 2011 (UTC)
Hi, regarding Germanic umlaut#Morphological effects, I still don't understand the umlaut progression from sit to set. In fall to fell I think I understand that fall took a suffix which caused the /ɔ/ (or a different vowel in the past tense?) to front to /ɛ/, after which the suffix disappeared. But in sit→ set, since sit is already fronted, what back vowel got fronted? Maybe just a little more detail would clarify it for me. Also, could you put in some more detail about the man → men progression -- was man originally /man/ and not /mæn/, so that /a/ got fronted to /ɛ/? Thanks. Duoduoduo ( talk) 23:40, 2 July 2011 (UTC)
I see you've recently made changes to collapse(topology). If t is a face of s, t has already two cofaces if t and s are distinct. Should the definition read t is a free face os s if t and s are the only cofaces of t in the complex? Thanks 132.236.54.92 ( talk) 19:17, 3 December 2011 (UTC)
I've copied this request here from Talk:Tensor#Understanding check on tensor type, since it does not relate to the article or its editing.
I have some assertions based on my present understanding of tensors, and if they're wrong, could someone explain why?
- My understanding is that a tensor with all the indices raised is contravariant and with all the indices lowered is covariant, and that the two tensors are dual Because a space of one-forms is a vector space, the dual to the all-covariant tensor should be the same as looking at the all-covariant tensor as an all-contravariant tensor in the dual space - each covariant index is contravariant relative to the dual space. So, if you represented each contravariant index by a vector, the covariant version would be that same set of vectors in the dual space. And vice versa - the level set representation of each covariant component is the same after taking the dual tensor and observing it in the dual space.
- Going on this I imagine raising and lowering indices as looking at pieces of an same object being pushed through a door between the collective vector and dual spaces, and when all the pieces are to one side or the other it looks the same from that side of the door (the two products of all non-dual spaces). ᛭ LokiClock ( talk) 22:50, 19 December 2011 (UTC)
- Since the object itself isn't altered by a change of basis, only its matrix representation, lowering a component and then applying a rotation will show the contravariant component moving against the rotation, and the covariant component moving in advance of the rotation (or is it equal?), but when you raise the index again it will be the same as if the rotation was applied with both indices contravariant ᛭ LokiClock ( talk) 22:50, 19 December 2011 (UTC)
You need to distinguish between finding the dual of a vector, and raising and lowering indices. They are not the same.
— Quondum t c 05:51, 20 December 2011 (UTC)
The easy questions first: Isolating the coefficients of a tensor with respect to a specific basis can be done via the dot product with each dual basis vector (this can be done for any basis, for a tensor of any order, with any mix of covariant and contravariant factor spaces). Anyhow, it should be clear that you get different scalar coefficients depending on whether you are dotting with the unprimed or primed basis:
This feels a little odd, each basis vector having its specific counterpart covector in the dual basis, yet there is no such thing as duality of standalone vectors in this sense. Also not to be confused with a myriad independent senses in which the term "dual" is used.
Yes, in Einstein notation the scalars with indices are the coefficients (or as everyone but me calls them them, components) for a specific basis. When you are dealing with numerical values, you have to make an actual choice of basis, but when you are dealing symbolically the actual choice can remain unspecified. This is complicated by the use of abstract index notation and the fact that usually there is no need to be clear whether this is being used, and you can even mix them freely if desired. They even look identical, except for a subtle indicator such as the use of Latin vs. Greek indices. The down side is potential confusion if you do not know which is intended, and there are times when you must be specific. So you could consistently write v = vb = vβeβ, where the Latin b (the abstract index notation) may be interpreted as an implied eb multiplied (via tensor product) with the term, and duplication of an abstract index implies contraction, not summation. Because the notation is so well-behaved, one generally does not have to worry whether an equation is as per Eintein (and hence dealing with scalars), or abstract (and hence representing the tensors themselves). I would not be surprized if many physicists are not clear on the distinction between the two notations.
I'll try to sketch typical transformations of the basis in a metric space. Imagine you have a vector basis and its covector dual. Being in a metric space allows us to refer to rotation, angles and length. Also, we can picture both the bases in the same space. Any collective rotation of the basis is matched by the same rotation, in the same direction, of the dual basis. Any collective scaling of the basis is matched by an inverse scaling of the dual basis. Any distortion of the basis (e.g. a scaling on one axis) is matched by the inverse distortion (an inverse scaling on the same axis), so if the angle between two basis vectors is reduced, the angle between duals increases. As to overlap between the basis and its dual, this occurs with an othonormal basis and its dual in a Euclidian space. It never occurs for an indefinite or a negative definite metric. In these cases, you can still get the dual being identical to the basis except for the appropriate number of its vectors being of the opposite sign. It is usual (at least in physics) to broaden the term orthonormal to allow these cases, where the basis vectors are orthogonal but the sqaure of these vectors may be in the set {+1, 0, −1}, thus allowing an "orthonormal" basis for any metric. — Quondum t c 07:31, 22 December 2011 (UTC)
If you want to undo the edit you can click "View history", then click on "00:22 5 December 2011, then click on "Edit" and then on "Save page". (Unless I have misunderstood what you wanted or the wiki software has been changed in some way I am not aware of.) - Haukur — Preceding unsigned comment added by 157.157.183.55 ( talk) 12:49, 24 January 2012 (UTC)
I'll respond on my talk page.-- 91.148.159.4 ( talk) 13:55, 24 January 2012 (UTC)
Hey, I really like your addition, distinguishing between "we share all properties" and "our structures share all of their properties." That's a very nice way to explain the difference between equality and isomorphism.— PaulTanenbaum ( talk) 15:17, 17 February 2012 (UTC)
By the way, I don't suppose it's surprising that a person who (a) describes himself as liking to learn and think about languages should also (b) be intrigued by isomorphism. At least that's the way it appears to this correspondent who loves learning and thinking about languages and is intriuged by isomorphism.— PaulTanenbaum ( talk) 18:42, 17 February 2012 (UTC)
[1] False. Let A = T ⊕ T where T is an arbitrary abelian group with at least one non-zero element of order ≠ 2. Let φ (x, y) = (y, x) and ψ (x, y) = (−x, y). Then φ∘ψ (x, y) = (y, −x) , but ψ∘φ (x, y) = (−y, x) . Ironically, two products with different order have exactly opposite signs, (i.e. anticommutator of these is zero, not commutator). Incnis Mrsi ( talk) 16:46, 7 March 2012 (UTC)
Hi LokiClock. I noticed you are one of few active editors to have meaningfully edited the Bach tensor article. I've recently made some major changes to the Lanczos tensor article. Perhaps you'd be interested in improving it or know someone else who is. Similar pages that could use some attention are Cotton tensor and Schouten tensor. Teply ( talk) 23:41, 13 October 2012 (UTC)
Hi! Thanks for your edit of Syntactic monoid#Syntactic equivalence. However, you changed the symbol of "left syntactic relation" (2nd def.), while the clarification request complained about "right syntactic equivalence" (1st def.) and "syntactic congruence" (3rd def.) looking the same. Therefore, in the new version, they still look the same. Maybe you intended to change the 1st or 3rd def.'s symbol? - Jochen Burghardt ( talk) 15:46, 8 February 2014 (UTC)
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Hi LokiClock. A long time ago I asked for help in rendering a few Old Norse names into IPA and you kindly gave your thoughts ( here and here). The thing is that you and User:Nora lives gave differing pronunciations, and I'd rather not mix and match the pronunciations you guys offered. Since Nora hasn't been around for a couple years, I was hoping you could show me in this table how you'd render these names and patronymics in IPA. That would give me a simple and consistent list to work with for articles relating to the 11th-century to 13th-century Kings of the Isles who regurgitated some of these. The last two are Old Norse forms of Gaelic names (the latter appears in Ágrip af Nóregskonungasǫgum [2]).
Name | IPA |
---|---|
Lǫgmaðr | non |
Óláfr Óláfsson | non |
Haraldr Haraldsson | non |
Guðrøðr Guðrøðarson | non |
Rǫgnvaldr Rǫgnvaldsson | non |
Magnús Magnússon | non |
Ragnhildr Óláfsdóttir | non |
Óspakr-Hákon | non |
Affrica Guðrøðardóttir | non |
Bjaðǫk | non |
Bjaðmunjo Mýrjartaksdóttir | non |
-- Brianann MacAmhlaidh ( talk) 00:31, 17 September 2016 (UTC)
Hello, LokiClock. Voting in the 2016 Arbitration Committee elections is open from Monday, 00:00, 21 November through Sunday, 23:59, 4 December to all unblocked users who have registered an account before Wednesday, 00:00, 28 October 2016 and have made at least 150 mainspace edits before Sunday, 00:00, 1 November 2016.
The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.
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Hi!
I anwsered to you on Talk:Cupola_(geometry)!
See you later! Padex ( talk) 17:21, 7 August 2009 (UTC)
Yes, the introduction seems to be an improvement. I'm still not entirely sure I know what it is, but I'm less unclear about how unclear I am now. ;-)- ( User) Wolfkeeper ( Talk) 03:20, 4 September 2009 (UTC)
I love the IPA and use it. The issue is its appropriate use in appropriate contexts.
So I must not ignore other editors, but they may ignore me. How does that work?
By the way, the correct idiom is "free rein," not "free reign." Wahrmund ( talk) 23:10, 10 November 2009 (UTC)
"and the distinction of <v> from <f> for medio-final /v/ to become merely etymological."
What do you mean? That the distinction is only made in the spelling and no longer in the language? Also, there was a medial distinction between /f/ and /v/ ('sævar' vs. 'sofa') but there wasn't any final distinction, was there? Haukur ( talk) 23:51, 28 November 2009 (UTC)
Thanks! Briangotts (Talk) (Contrib) 14:51, 30 November 2009 (UTC)
Hello. In case you didn't know, when you add content to talk pages and Wikipedia pages that have open discussion, you should sign your posts by typing four tildes ( ~~~~ ) at the end of your comment. You may also click on the signature button located above the edit window. This will automatically insert a signature with your username or IP address and the time you posted the comment. This information is useful because other editors will be able to tell who said what, and when. Thank you. -- SineBot ( talk) 09:04, 1 December 2009 (UTC)
I didn't remove any references, I merely moved the speculation about Þorodd out of the first paragraph of the article... AnonMoos ( talk) 03:56, 27 December 2009 (UTC)
See Talk:First Grammatical Treatise. AnonMoos ( talk) 23:57, 28 December 2009 (UTC)
Please refer to WP:MOSMATH. Periods go inside the math tags. Sławomir Biały ( talk) 02:07, 31 December 2009 (UTC)
Huh? Sorry, but those comments are old, and I'm really not sure which comment you´re referring to. But I cannot see any claim from me that dansk tunga wasn't used about the Danish language as it was spoken then. Icelandic court documents from the 10th century referred to dansk tunga and Snorrí also used the term dansk tunga. I'm perfectly aware that the language spoken in the north-germanic areas was called danish by it's speakers (tongue being synomym to language as in Icelandic tungumál, Danish tungemål). As far as I can see I'm only discussing the correct use of danish tongue and whether it can be used about Old Norwegian and Old Icelandic if the term Old Norse only refers to those dialects. Of course you may think of a completely different comment, in which case my reply is pure nonsense ;) Dylansmrjones ( talk) 21:45, 2 February 2010 (UTC)
The Original Barnstar | ||
I award LokiClock this barnstar for his enthusiastic contributions to articles on the Old Norse language. Haukur ( talk) 20:24, 7 February 2010 (UTC) |
Please don't add {{ stub}} tags to articles such as Málaháttr when they already have a subject-specific stub tag. And when you're adding stub tags, please put them at the end, as per WP:LAYOUT, not at the start. Thanks. PamD ( talk) 22:11, 21 April 2010 (UTC)
This is a courtesy note to let you know that the C++0x#Criticisms section you added is still empty, and that the discussion on the talk page may result in it being deleted on Jun 18 2010, if there is no sourced content in it at that time. -- Sacolcor ( talk) 15:28, 4 June 2010 (UTC)
Part of a series on |
Old Norse |
---|
WikiProject Norse history and culture |
G'day, I've noticed that you're quite active on Old Norse articles, so I thought you might be interested in this template. Feel free to add, remove, or rearrange things. Hayden120 ( talk) 05:31, 17 June 2010 (UTC)
I have added the "reviewers" property to your user account. This property is related to the Pending changes system that is currently being tried. This system loosens page protection by allowing anonymous users to make "pending" changes which don't become "live" until they're "reviewed". However, logged-in users always see the very latest version of each page with no delay. A good explanation of the system is given in this image. The system is only being used for pages that would otherwise be protected from editing.
If there are "pending" (unreviewed) edits for a page, they will be apparent in a page's history screen; you do not have to go looking for them. There is, however, a list of all articles with changes awaiting review at Special:OldReviewedPages. Because there are so few pages in the trial so far, the latter list is almost always empty. The list of all pages in the pending review system is at Special:StablePages.
To use the system, you can simply edit the page as you normally would, but you should also mark the latest revision as "reviewed" if you have looked at it to ensure it isn't problematic. Edits should generally be accepted if you wouldn't undo them in normal editing: they don't have obvious vandalism, personal attacks, etc. If an edit is problematic, you can fix it by editing or undoing it, just like normal. You are permitted to mark your own changes as reviewed.
The "reviewers" property does not obligate you to do any additional work, and if you like you can simply ignore it. The expectation is that many users will have this property, so that they can review pending revisions in the course of normal editing. However, if you explicitly want to decline the "reviewer" property, you may ask any administrator to remove it for you at any time. — Carl ( CBM · talk) 12:33, 18 June 2010 (UTC) — Carl ( CBM · talk) 13:29, 18 June 2010 (UTC)
Why did you revert my addition of <ǿ> to the transcription list? My authority for stating that this is a modern, scholarly way of representing /ø:/ in Old Norse is Terje Spurkland: "Innføring i norrønt språk", Universitetsforlaget, 9th edition (2007). This is the standard textbook in Old Norse at the University of Oslo. From a typographical point of view, I too prefer <œ>, but that doesn't change the fact. Devanatha ( talk) 16:31, 6 July 2010 (UTC)
IMO Putting Wylie and IPA together like this tends to confuse the difference between a transliteration system (Wylie) and a transcription (IPA) system. The IPA transcription of the sounds of the isolated Tibetan consonants more properly belongs in the article on the Tibetan script ~ perhaps we should insert the IPA transcriptions there and provide a link?. In his original article on the system Turrell V. Wylie did not detail the sounds of the letters - though he did mistakenly call the system he outlined Tibetan transcription. Can we just put the IPA in the article on Tibetan script and then remove it in the Wylie transliteration article? Chris Fynn ( talk) 10:11, 29 August 2010 (UTC)
Why did you remove this table from Old Norse orthography? Although the orthography of Old Norse was not completely consistent, the table still gave a general idea of the consonants and the Latin graphemes that were used to represent them. This is not covered anywhere else in the article – only vowels are covered. Thanks, Hayden120 ( talk) 06:15, 18 October 2010 (UTC)
I responded on my talk page. Benwing ( talk) 10:16, 17 May 2011 (UTC)
Hi, regarding Germanic umlaut#Morphological effects, I still don't understand the umlaut progression from sit to set. In fall to fell I think I understand that fall took a suffix which caused the /ɔ/ (or a different vowel in the past tense?) to front to /ɛ/, after which the suffix disappeared. But in sit→ set, since sit is already fronted, what back vowel got fronted? Maybe just a little more detail would clarify it for me. Also, could you put in some more detail about the man → men progression -- was man originally /man/ and not /mæn/, so that /a/ got fronted to /ɛ/? Thanks. Duoduoduo ( talk) 23:40, 2 July 2011 (UTC)
I see you've recently made changes to collapse(topology). If t is a face of s, t has already two cofaces if t and s are distinct. Should the definition read t is a free face os s if t and s are the only cofaces of t in the complex? Thanks 132.236.54.92 ( talk) 19:17, 3 December 2011 (UTC)
I've copied this request here from Talk:Tensor#Understanding check on tensor type, since it does not relate to the article or its editing.
I have some assertions based on my present understanding of tensors, and if they're wrong, could someone explain why?
- My understanding is that a tensor with all the indices raised is contravariant and with all the indices lowered is covariant, and that the two tensors are dual Because a space of one-forms is a vector space, the dual to the all-covariant tensor should be the same as looking at the all-covariant tensor as an all-contravariant tensor in the dual space - each covariant index is contravariant relative to the dual space. So, if you represented each contravariant index by a vector, the covariant version would be that same set of vectors in the dual space. And vice versa - the level set representation of each covariant component is the same after taking the dual tensor and observing it in the dual space.
- Going on this I imagine raising and lowering indices as looking at pieces of an same object being pushed through a door between the collective vector and dual spaces, and when all the pieces are to one side or the other it looks the same from that side of the door (the two products of all non-dual spaces). ᛭ LokiClock ( talk) 22:50, 19 December 2011 (UTC)
- Since the object itself isn't altered by a change of basis, only its matrix representation, lowering a component and then applying a rotation will show the contravariant component moving against the rotation, and the covariant component moving in advance of the rotation (or is it equal?), but when you raise the index again it will be the same as if the rotation was applied with both indices contravariant ᛭ LokiClock ( talk) 22:50, 19 December 2011 (UTC)
You need to distinguish between finding the dual of a vector, and raising and lowering indices. They are not the same.
— Quondum t c 05:51, 20 December 2011 (UTC)
The easy questions first: Isolating the coefficients of a tensor with respect to a specific basis can be done via the dot product with each dual basis vector (this can be done for any basis, for a tensor of any order, with any mix of covariant and contravariant factor spaces). Anyhow, it should be clear that you get different scalar coefficients depending on whether you are dotting with the unprimed or primed basis:
This feels a little odd, each basis vector having its specific counterpart covector in the dual basis, yet there is no such thing as duality of standalone vectors in this sense. Also not to be confused with a myriad independent senses in which the term "dual" is used.
Yes, in Einstein notation the scalars with indices are the coefficients (or as everyone but me calls them them, components) for a specific basis. When you are dealing with numerical values, you have to make an actual choice of basis, but when you are dealing symbolically the actual choice can remain unspecified. This is complicated by the use of abstract index notation and the fact that usually there is no need to be clear whether this is being used, and you can even mix them freely if desired. They even look identical, except for a subtle indicator such as the use of Latin vs. Greek indices. The down side is potential confusion if you do not know which is intended, and there are times when you must be specific. So you could consistently write v = vb = vβeβ, where the Latin b (the abstract index notation) may be interpreted as an implied eb multiplied (via tensor product) with the term, and duplication of an abstract index implies contraction, not summation. Because the notation is so well-behaved, one generally does not have to worry whether an equation is as per Eintein (and hence dealing with scalars), or abstract (and hence representing the tensors themselves). I would not be surprized if many physicists are not clear on the distinction between the two notations.
I'll try to sketch typical transformations of the basis in a metric space. Imagine you have a vector basis and its covector dual. Being in a metric space allows us to refer to rotation, angles and length. Also, we can picture both the bases in the same space. Any collective rotation of the basis is matched by the same rotation, in the same direction, of the dual basis. Any collective scaling of the basis is matched by an inverse scaling of the dual basis. Any distortion of the basis (e.g. a scaling on one axis) is matched by the inverse distortion (an inverse scaling on the same axis), so if the angle between two basis vectors is reduced, the angle between duals increases. As to overlap between the basis and its dual, this occurs with an othonormal basis and its dual in a Euclidian space. It never occurs for an indefinite or a negative definite metric. In these cases, you can still get the dual being identical to the basis except for the appropriate number of its vectors being of the opposite sign. It is usual (at least in physics) to broaden the term orthonormal to allow these cases, where the basis vectors are orthogonal but the sqaure of these vectors may be in the set {+1, 0, −1}, thus allowing an "orthonormal" basis for any metric. — Quondum t c 07:31, 22 December 2011 (UTC)
If you want to undo the edit you can click "View history", then click on "00:22 5 December 2011, then click on "Edit" and then on "Save page". (Unless I have misunderstood what you wanted or the wiki software has been changed in some way I am not aware of.) - Haukur — Preceding unsigned comment added by 157.157.183.55 ( talk) 12:49, 24 January 2012 (UTC)
I'll respond on my talk page.-- 91.148.159.4 ( talk) 13:55, 24 January 2012 (UTC)
Hey, I really like your addition, distinguishing between "we share all properties" and "our structures share all of their properties." That's a very nice way to explain the difference between equality and isomorphism.— PaulTanenbaum ( talk) 15:17, 17 February 2012 (UTC)
By the way, I don't suppose it's surprising that a person who (a) describes himself as liking to learn and think about languages should also (b) be intrigued by isomorphism. At least that's the way it appears to this correspondent who loves learning and thinking about languages and is intriuged by isomorphism.— PaulTanenbaum ( talk) 18:42, 17 February 2012 (UTC)
[1] False. Let A = T ⊕ T where T is an arbitrary abelian group with at least one non-zero element of order ≠ 2. Let φ (x, y) = (y, x) and ψ (x, y) = (−x, y). Then φ∘ψ (x, y) = (y, −x) , but ψ∘φ (x, y) = (−y, x) . Ironically, two products with different order have exactly opposite signs, (i.e. anticommutator of these is zero, not commutator). Incnis Mrsi ( talk) 16:46, 7 March 2012 (UTC)
Hi LokiClock. I noticed you are one of few active editors to have meaningfully edited the Bach tensor article. I've recently made some major changes to the Lanczos tensor article. Perhaps you'd be interested in improving it or know someone else who is. Similar pages that could use some attention are Cotton tensor and Schouten tensor. Teply ( talk) 23:41, 13 October 2012 (UTC)
Hi! Thanks for your edit of Syntactic monoid#Syntactic equivalence. However, you changed the symbol of "left syntactic relation" (2nd def.), while the clarification request complained about "right syntactic equivalence" (1st def.) and "syntactic congruence" (3rd def.) looking the same. Therefore, in the new version, they still look the same. Maybe you intended to change the 1st or 3rd def.'s symbol? - Jochen Burghardt ( talk) 15:46, 8 February 2014 (UTC)
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Hi LokiClock. A long time ago I asked for help in rendering a few Old Norse names into IPA and you kindly gave your thoughts ( here and here). The thing is that you and User:Nora lives gave differing pronunciations, and I'd rather not mix and match the pronunciations you guys offered. Since Nora hasn't been around for a couple years, I was hoping you could show me in this table how you'd render these names and patronymics in IPA. That would give me a simple and consistent list to work with for articles relating to the 11th-century to 13th-century Kings of the Isles who regurgitated some of these. The last two are Old Norse forms of Gaelic names (the latter appears in Ágrip af Nóregskonungasǫgum [2]).
Name | IPA |
---|---|
Lǫgmaðr | non |
Óláfr Óláfsson | non |
Haraldr Haraldsson | non |
Guðrøðr Guðrøðarson | non |
Rǫgnvaldr Rǫgnvaldsson | non |
Magnús Magnússon | non |
Ragnhildr Óláfsdóttir | non |
Óspakr-Hákon | non |
Affrica Guðrøðardóttir | non |
Bjaðǫk | non |
Bjaðmunjo Mýrjartaksdóttir | non |
-- Brianann MacAmhlaidh ( talk) 00:31, 17 September 2016 (UTC)
Hello, LokiClock. Voting in the 2016 Arbitration Committee elections is open from Monday, 00:00, 21 November through Sunday, 23:59, 4 December to all unblocked users who have registered an account before Wednesday, 00:00, 28 October 2016 and have made at least 150 mainspace edits before Sunday, 00:00, 1 November 2016.
The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail.
If you wish to participate in the 2016 election, please review the candidates' statements and submit your choices on the voting page. MediaWiki message delivery ( talk) 22:08, 21 November 2016 (UTC)
Hi LokiClock! You're receiving this notification because you were previously listed at Wikipedia:WikiProject History/Outreach/Participants, but you haven't made any edits to the English Wikipedia in over 6 months.
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