From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: eigenvalue of A+A'
Date: 10 Jul 1998 22:15:36 GMT

In article <35A61AD6.4B86@et.htwk-leipzig.de>,
Hendrik Richter  <hrichte@et.htwk-leipzig.de> wrote:

>I'm looking for a relation between the eigenvalues
>of a real square matrix A and the eigenvalues of the matrix
>A+A' (' stands for transpose).
>Can there be said something in general;

Not in too much generality; how much information can you recover about
the eigenvalues of  A  from the eigenvalues of  A+A'  if  A  is
skew-symmetric? 

In general, we may write any matrix  A  as a sum  A = A1 + A2  with  
A1  symmetric, A2 skew-symmetric; you're asking for the relationship 
between the eigenvalues of  A  and those of  A1.
Well, they agree if  A2=0, and as you vary  A2  they change continuously;
you could estimate the changes, I guess, if you knew something about
how close  A  was to A1. Is that the kind of information you seek?

dave