Talk:Inverse element

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Geometry guy 21:20, 9 July 2007 (UTC)

[edit] 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):

why det=0 => no one-sided inverse ?
why "no one-sided inverse" => "l/r inverse implies existence of the other" ?
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 Apr 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://aktzin.com/InverseDemo.jsp page. Should I create a wikipedia page to describe the algorithm?

The original matrix was:

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