# A Ring Isomorphism and corresponding Pseudoinverses

Authors
Type
Preprint
Publication Date
Oct 01, 2008
Submission Date
Oct 01, 2008
Identifiers
arXiv ID: 0810.0093
Source
arXiv
This paper studies the set of $n\times n$ matrices for which all row and column sums equal zero. By representing these matrices in a lower dimensional space, it is shown that this set is closed under addition and multiplication, and furthermore is isomorphic to the set of arbitrary $(n-1)\times (n-1)$ matrices. The Moore-Penrose pseudoinverse corresponds with the true inverse, (when it exists), in this lower dimension and an explicit representation of this pseudoinverse in terms of the lower dimensional space is given. This analysis is then extended to non-square matrices with all row or all column sums equal to zero.