Talk:Inverse element

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
 Field: Algebra

left/right matrix inverse[edit]

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 Apr 2005 (UTC)


I disagree...

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

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

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

The null-space for this matrix is:

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:

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

The null space is the same as the above:

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