Re: Eigenvalue of symmetric matrix
From: Robert Israel (israel_at_math.ubc.ca)
Date: 07/19/04
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Date: Mon, 19 Jul 2004 18:44:03 +0000 (UTC)
In article <cdgmnh$5uk$1@news.ks.uiuc.edu>,
Hardy B. Siahaan <hardy.siahaan@itk.ntnu.no> wrote:
>1. Given is any real matrix A of size n by n where A+A' does not have
>complex conjugate eigenvalue(s).
Assuming A' is the transpose of A, A+A' is a real symmetric matrix,
so its eigenvalues are all real.
> Let's denote the maximum eigenvalue
>of (A+A') as c_max(A).
>Is there any function f(A) which can be used as upperbound for
>c_max(A), i.e. c_max(A) \leq f(A), where f(A) is a function of
>eigenvalue(s) of A?
Not a function of the eigenvalues of A. For example,
the only eigenvalue of
[ 0 r ]
A = [ 0 0 ]
is 0, but c_max(A) = |r|.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2
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