Talk:Inverse element

left/right matrix inverse

I think the phrase

If the determinant of M is zero, it is impossible for it to have a one-sided inverse; therefore a left inverse or right inverse implies the existence of the other one.

is redundant, and not very clear, (IMHO):

1. why det=0 => no one-sided inverse ?
2. why "no one-sided inverse" => "l/r inverse implies existence of the other" ?
3. more specifically, why is a left inverse matrix also is a right inverse ?

But as I already did some "cutting", I'll leave it for the moment... MFH 15:17, 5 April 2005 (UTC)

I disagree...

This problem stated on this page is slightly confusing to me:

${\begin{bmatrix}17&22&27\\22&29&36\\27&36&45\end{bmatrix}}$

The statement above that this "Is a singular matrix, and can't be inverted." is partly incorrect.

An inverse is shown here:

${\begin{bmatrix}1.25&0.0&-0.75\\0.0&0.0&0.0\\-0.75&0.0&0.47222\end{bmatrix}}$

This matrix is a left and right hand inverse (Moore-Penrose properties 1 and 2).

The null-space for this matrix is:

${\begin{bmatrix}0.0&-0.5&0.0\\0.0&1.0&0.0\\0.0&-0.5&0.0\end{bmatrix}}$

There are an infinite number of solutions to the underspecified or singular matrix. The calculations are not difficult and are described on the http://mjollnir.com/matrix/demo.html page. Should I create a wikipedia page to describe the algorithm?

The original matrix was:

${\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}}$

Using the http://mjollnir.com/matrix/demo.html site online calculator, a pseudo-inverse is directly calculated:

${\begin{bmatrix}-1.0&0.5\\0.0&0.0\\0.666667&-0.166667\end{bmatrix}}$

The null space is the same as the above:

${\begin{bmatrix}0.0&-0.5&0.0\\0.0&1.0&0.0\\0.0&-0.5&0.0\end{bmatrix}}$

rand huso (talk) 18:08, 23 February 2008 (UTC)

Unencyclopedic tone

Instead of considered first the most common uses of "inverse element", the article focuses to the widest generalizations of the concept, which are rarely considered outside the advanced study of pure algebraic structures. It results the article is not only too WP:TECHNICAL, but readers, specially those who come here through one of the many links to Invertible, do not find here what they are looking for.

I have recently rewritten the lead for summarizing what should be in this article and providing the basic information to the readers, and I'll start to rewrite the body of the article. However, this is not my highest priority, so it is possible that the article will have a strange structure for some time. D.Lazard (talk) 10:36, 11 March 2022 (UTC)

"Invertible element" listed at Redirects for discussion

An editor has identified a potential problem with the redirect Invertible element and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 December 10 § Invertible element until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Jay 💬 16:21, 10 December 2022 (UTC)