Editing Division by zero (section)

===Linear algebra===
In [[matrix (mathematics)|matrix]] algebra, square or rectangular blocks of numbers are manipulated as though they were numbers themselves: matrices can be [[matrix addition|added]] and [[matrix multiplication|multiplied]], and in some cases, a version of division also exists. Dividing by a matrix means, more precisely, multiplying by its [[Invertible matrix|inverse]]. Not all matrices have inverses.<ref>{{citation|last=Gbur |first=Greg |author-link=Greg Gbur |title=Mathematical Methods for Optical Physics and Engineering |pages=88–93 |year=2011 |isbn=978-0-521-51610-5 |publisher=Cambridge University Press|bibcode=2011mmop.book.....G }}</ref> For example, a [[zero matrix|matrix containing only zeros]] is not invertible.

One can define a pseudo-division, by setting ''a''/''b''&nbsp;=&nbsp;''ab''<sup>+</sup>, in which ''b''<sup>+</sup> represents the [[Moore–Penrose inverse|pseudoinverse]] of ''b''. It can be proven that if ''b''<sup>−1</sup> exists, then ''b''<sup>+</sup> = ''b''<sup>−1</sup>. If ''b'' equals 0, then b<sup>+</sup> = 0.