Talk:Invertible matrix

message: Sorry to say so, but I think this page is too complicated.
Example from the introduction:
"Over the field of real numbers, the set of singular n-by-n matrices, considered as a subset of R^{n \times n}, is a null set, i.e., has Lebesgue measure zero. (This is true because singular matrices can be thought of as the roots of the polynomial function given by the determinant.) "
Who cares?  Sure, this may be an interesting aside, but it obfuscates more important things.  In particular, since the "matrix inverse" page has been merged here, the extremely useful content that used to reside there should be clearer.
I have referred to Wikipedia's "matrix inverse" page innumerable times in the past to remind me how to do simple matrix inversion. (I forget these things!)  Now when I look for that simple information I get overloaded with nonsense about the Lebesque measure of the set of singular matrices.  Seriously?
Wikipedia used to be a good source for the basic explaination. If I needed more, I'd go to Mathworld- which was not very often, since I never understood what Wolfram was saying!
My request to the fantastic math heads writing this page: put the high-school stuff first, since that's what a lot people will want to see.  Make it clear to people with minimum math background, and keep it simple when possible.
Thanks for the hard work. I'm just trying to help make the information useful for everyone.
Hawkeyek (talk) 05:51, 10 April 2008 (UTC)
replies: text: The purpose is to say that singular (non-invertible) matrices are very very very rare. If you choose a matrix with random real entries (say, between 0 and 1), then the probability it is singular is literally zero. That is not to say that non-invertible matrices can't happen, just that they are infinitely unlikely. (if this seems like a contradiction, consider throwing a dart at a dartboard - what is the probability that the dart will hit a particular point?) 67.9.148.47 (talk) 11:50, 28 November 2008 (UTC)

text: I think this information is important to include, but that earlier in the article we can describe it in simpler terms, such as those used by 67.9.148.47 above. Dcoetzee 08:46, 29 November 2008 (UTC)
replies: text: I think it is important to include that singularity is rare. Maybe we should add something small to make sure we're not overgeneralizing.  Singularity over a euclidean field is rare. But isn't a square matrix over z2 almost always singular?   — Preceding unsigned comment added by 132.235.46.80 (talk) 04:05, 9 November 2011 (UTC)
replies: text: Prompted by the discussion here, I have moved it to later.  It does not seem to be important enough to be in the lead of the article.  Incidentally, the lead doesn't exactly comply with the WP:LEAD guideline anyway.  It should probably be rewritten and the existing content relocated elsewhere. siℓℓy rabbit (talk) 13:53, 29 November 2008 (UTC)
replies: text: Could someone add a simple example with real numbers? That was what I was looking for, just some actual example not involving variables. — Preceding unsigned comment added by 60.166.111.122 (talk) 14:19, 16 September 2015 (UTC)
thread_title:  Sigh 

message: The statement that "It is crucial for the matrix H to be invertible for the receiver to be able to figure out the transmitted information." is just plain wrong. The matrix H is not always square, and there are several better ways of decoding the transmitted signal, instead of inverting the channel matrix. I have never edited a Wikipedia page before, so I will figure that out before I make some correcting changes.  — Preceding unsigned comment added by 89.160.119.209 (talk) 11:00, 13 December 2013 (UTC)
thread_title:  Matrix inverses in MIMO wireless communication 

message: A square matrix is singular if and only if it's determinant is zero.
A family of vectors are linearly independent if and only if the determinant of their matrix is zero.
I really think there should be a mention of linear independence here after the reference to singular matrices since singularity is equivalent to linear dependence, which also ties in to the discussion later about eigenvectors and such. There's already a page on linear independence so just a quick link would be nice.
SomeHandyGuy (talk) 00:33, 4 June 2014 (UTC)
thread_title:  No mention of linear independence anywhere 

message: I think those phrases would appear more in text, i.e. someone reading and clicking wants to know what is an "inverse matrix", or how do I invert a matrix. 
Would it make sense to rename and reword this article? :-
"The inverse of a matrix 'A' is a matrix 'B' such that ... AB=I ; a matrix for which such an inverse exists is called 'invertible'..."
Fmadd (talk) 08:38, 4 February 2017 (UTC)
thread_title:  Article Name: why not '''inverse matrix''' or '''matrix inverse''' ? 

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thread_title:  External links modified 

message: Somehow the formula for the inverse of a general 2x2 matrix is not showing correctly. The latex has a minus before the c but the output does not. I can't seem to fix it.— Preceding unsigned comment added by 92.194.124.84 (talk) 15:18, 14 January 2021 (UTC)
replies: text: Thank you for your concern about the minus signs, but Wikipedia has a software bug.  Editors have tried several times to kludge it to no avail. This has been reported multiple times now on WP:VPT. We'll just have to wait until the administrators fix it properly.—Anita5192 (talk) 16:57, 14 January 2021 (UTC)
thread_title:  Formula not showing correctly 

message: The redirect Nonsingular has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  1234qwer1234qwer4 23:04, 25 April 2023 (UTC)
thread_title:  "[[:Nonsingular]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]