About the logarithm function over the matrices

Details About the logarithm function over the matrices About the logarithm function over the matrices

2007-12-04

arxiv.org/abs/0712.0410v2

Mathematics

Rings and Algebras

Minor corrections and a new result

Scientific paper

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.

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