Re: Eigenvalue of symmetric matrix
From: Hardy B. Siahaan (hardy.siahaan_at_itk.ntnu.no)
Date: 07/19/04
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Date: Mon, 19 Jul 2004 18:44:02 +0000 (UTC)
Sorry, I made a mistake on the question.
Correction to the problem:
Given is any real matrix A of size n by n. 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?
Hardy
On Mon, 19 Jul 2004 14:44:01 +0000 (UTC), Hardy B. Siahaan wrote:
>1. Given is any real matrix A of size n by n where A+A' does not have
>complex conjugate eigenvalue(s). 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?
>2. Given is any real matrix M of size n by n. Denote the real part of
>the maximum eigenvalue of (M+M') as r_max(M).
>Is there any function g(M) which can be used as upperbound for
>r_max(M), i.e. r_max(M) \leq g(M), where g(M) is a function of
>eigenvalue(s) of M?
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