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[Octave-bug-tracker] [bug #51246] pinv(0) different from Matlab

From: Travis Arnold
Subject: [Octave-bug-tracker] [bug #51246] pinv(0) different from Matlab
Date: Fri, 6 Apr 2018 13:47:45 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/65.0.3325.181 Safari/537.36

Follow-up Comment #19, bug #51246 (project octave):

It looks like this has been resolved, but nevertheless I'd like to chime in.

In reference to comment 4:

"I would still open a discussion on Octave Maintainers list just to see if
there is a good mathematical reason for returning either 0 or Inf. "

There is a good mathematical reason for returning pinv(0) = 0. Although there
are different mathematical notions of generalized inverse, the most widely
used is the Moore-Penrose inverse
(https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse). For any matrix
A, there exists a unique matrix B with the following four properties:

0  A*B*A = A 
0  B*A*B = B 
0  A*B is Hermitian 
0  B*A is Hermitian 

B is the Moore-Penrose inverse of A. It is easy to verify that the
Moore-Penrose inverse of a zero matrix is a zero matrix.

If you look at the documentation of pinv in Matlab, this is precisely what is
returned there. This is what Octave should return as well.


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