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Should it be mentioned that Schur's complement is produced by Gauss-reducing the matrix M for all the pivots in D? That's what it is about isn't it, what linear regression does to the variance matrix - Martin Vermeer
There, it is claimed that:
the conditional variance of X given Y is the Schur complement of C in V:
To me, is a function of the random variable ; hence a random variable itself. I don't' see any -dependence above, so to me, the implication is that this function is constant for all values of ; is this a consequence of the normality assumption? Btyner 22:18, 10 February 2006 (UTC)
This article's definition implies both of the following: Let
so that M is a (p+q)×(p+q) matrix.
Then the Schur complement of the block D of the matrix M is the p×p matrix
and the Schur complement of the block A of the matrix M is the q×q matrix
I'll dig out Strang's book on Tuesday and see what it says. Michael Hardy ( talk) 23:42, 19 January 2008 (UTC)
It'd be nice to setup Ax=b, for a 2x2 matrix, and then use the schur complement to show what the values of x_1 and x_2 are -- 131.215.105.118 ( talk) 18:48, 16 November 2007 (UTC)
Star-mesh transform states:
My visit here didn't help me much, not having done any linear algebra for thirty years. — MaxEnt 13:51, 2 April 2014 (UTC)
Does anyone have a reference for the quotient notation,
which entered into the article here? Is it standard? I have not seen this before and have been working with Schur complements for a long time. I'm not particularly for or against it, but it does seem non-standard. One potential point of confusion for readers is that it conflicts with the notation in Matlab/Octave, wherein means . 128.62.208.237 ( talk) 19:18, 9 April 2019 (UTC)
The Section "Application to solving linear equations" and the second part of "Background" (introduced in https://en.wikipedia.org/?title=Schur_complement&oldid=1009008699) seem to overlap significantly and repeat each other. I am not sure about the added value of the new material in the 2nd part of "Background", but I am not going to butcher it. However, I think the 2nd part of "Background" should be curtailed to several written sentences and refer extensively to "Application to solving linear equations" section, and all additional equations from the 2nd part of "Background" should be moved to "Application to solving linear equations" if appropriate. Any comments, @ Hnsymjh:? AVM2019 ( talk) 19:21, 26 June 2021 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
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To-do list for Schur complement:
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Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
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Should it be mentioned that Schur's complement is produced by Gauss-reducing the matrix M for all the pivots in D? That's what it is about isn't it, what linear regression does to the variance matrix - Martin Vermeer
There, it is claimed that:
the conditional variance of X given Y is the Schur complement of C in V:
To me, is a function of the random variable ; hence a random variable itself. I don't' see any -dependence above, so to me, the implication is that this function is constant for all values of ; is this a consequence of the normality assumption? Btyner 22:18, 10 February 2006 (UTC)
This article's definition implies both of the following: Let
so that M is a (p+q)×(p+q) matrix.
Then the Schur complement of the block D of the matrix M is the p×p matrix
and the Schur complement of the block A of the matrix M is the q×q matrix
I'll dig out Strang's book on Tuesday and see what it says. Michael Hardy ( talk) 23:42, 19 January 2008 (UTC)
It'd be nice to setup Ax=b, for a 2x2 matrix, and then use the schur complement to show what the values of x_1 and x_2 are -- 131.215.105.118 ( talk) 18:48, 16 November 2007 (UTC)
Star-mesh transform states:
My visit here didn't help me much, not having done any linear algebra for thirty years. — MaxEnt 13:51, 2 April 2014 (UTC)
Does anyone have a reference for the quotient notation,
which entered into the article here? Is it standard? I have not seen this before and have been working with Schur complements for a long time. I'm not particularly for or against it, but it does seem non-standard. One potential point of confusion for readers is that it conflicts with the notation in Matlab/Octave, wherein means . 128.62.208.237 ( talk) 19:18, 9 April 2019 (UTC)
The Section "Application to solving linear equations" and the second part of "Background" (introduced in https://en.wikipedia.org/?title=Schur_complement&oldid=1009008699) seem to overlap significantly and repeat each other. I am not sure about the added value of the new material in the 2nd part of "Background", but I am not going to butcher it. However, I think the 2nd part of "Background" should be curtailed to several written sentences and refer extensively to "Application to solving linear equations" section, and all additional equations from the 2nd part of "Background" should be moved to "Application to solving linear equations" if appropriate. Any comments, @ Hnsymjh:? AVM2019 ( talk) 19:21, 26 June 2021 (UTC)