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 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