|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
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)
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: