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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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**[Octave-bug-tracker] [bug #51246] pinv(0) different from Matlab**,
*Travis Arnold* **<=**