About the logarithm function over the matrices
Rings and Algebras
2007-12-20 v2
Abstract
We prove the following results: let x,y be (n,n) complex matrices such that x,y,xy have no eigenvalue in ]-infinity,0] and log(xy)=log(x)+log(y). If n=2, or if n>2 and x,y are simultaneously triangularizable, then x,y commute. In both cases we reduce the problem to a result in complex analysis.
Cite
@article{arxiv.0712.0410,
title = {About the logarithm function over the matrices},
author = {Bourgeois Gerald},
journal= {arXiv preprint arXiv:0712.0410},
year = {2007}
}
Comments
Minor corrections and a new result