From: israel@math.ubc.ca (Robert Israel)
Subject: Re: Real Matrix log
Date: 8 Feb 2001 23:58:23 GMT
Newsgroups: sci.math
Summary: Which matrices have 'logarithms' ?

In article <95v5a8$gq9$1@nnrp1.deja.com>,  <azmi_tamid@my-deja.com> wrote:
>Which n by n real matrices A can be written as A= e^(B) where B is also
>n by n real matrix ?

The requirements are, I think:

1) A is nonsingular
2) For each negative eigenvalue -r, the dimensions of the spaces
{x: (A + rI)^k x = 0} are all even. 

Robert Israel                                israel@math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel 
University of British Columbia            
Vancouver, BC, Canada V6T 1Z2