Talk:Matrix determinant lemma

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a couple of questions[edit]

Entropeneur, you post an inline cite to the "Matrix Reference Manual" for the name "matrix determinant lemma" but no such name appears there. Do you have a reference for the name you chose for the article?

Also, you cited "Numerical Recipes" later in the text. What is that cite supposed to be for? The section you cited is about the Sherman-Morrison and the Woodbury formula. The subject of this article doesn't appear there, and the sentence you tagged (about using unit vectors?) doesn't appear there either. Lunch 20:44, 18 May 2007 (UTC)[reply]

Response to questions from Lunch[edit]

- 'Matrix determinant lemma' name: This name appears here: http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/identity.html It does seem that this name is obscure, Google returns just 5 hits in total for "matrix determinant lemma". I would have no particular objection to changing the title of this article.

- Cite of 'Numerical Recipes in C': I was referring just to the ability of u and v to effect row, column or element updates to the matrix. This is why the reference was inserted mid-sentence. Entropeneur 09:04, 21 May 2007 (UTC)[reply]

==

Is this not related to the Weinstein-Aronszajn identity? Their identity states that for an $n$ by $r$ matrix $V$ and an $n$ matrix $A$ we have

${\rm {det}}(\lambda I_{n}-(A+VV^{T}))/{\rm {det}}(\lambda I_{n}-A)={\rm {det}}(1_{r}-V^{T}(\lambda I-A)^{-1}V)$

Mike Stone (talk) 21:25, 7 November 2011 (UTC)[reply]

Merger proposal[edit]

I could not find the term in the book by Harville. I don't think many (or any?) published resources use the term "matrix determinant lemma". And although the identity is useful, the proof is not hard, and I don't think one identity deserves its own article, hence I proposed to merge it with the determinant article, under a relevant "identity" section. Improbable keeler (talk) 15:06, 12 November 2013 (UTC)[reply]

Sighting: The Matrix Determinant Lemma

Despite this sighting, it does not appear to be a standard phrase, though it might benefit from better publicity in its own right. If it's going to be badly buried by merge into a large page (I didn't look) then I would hesitate, otherwise I think your argument is valid.

Note that I renamed this section so that the "discuss" link functions correctly. — MaxEnt 22:40, 3 April 2014 (UTC)[reply]

I propose that it be merged with Sylvester determinant theorem instead. It looks like a corollary to that one, or a minor variation, and the proofs are strikingly similar. Marc van Leeuwen (talk) 15:05, 15 April 2014 (UTC)[reply]

I agree that merging with determinant, which is already a long article, might not be so good. Merging with Sylvester's determinant theorem seems a good idea, and I was about to do this, but then I noticed that Talk:Sylvester's determinant theorem rightly notes that all the references (except for the slightly dubious MathWorld one) actually talk about quite a different determinant identity. I guess we should fix that first. -- Jitse Niesen (talk) 09:03, 1 August 2014 (UTC)[reply]