Subject: Math Problem: Polynomials and Matrices

From: "G. Matthias Ullmann" <[email-masked]>
Date: Tue, 29 Feb 2000 11:34:23 -0800

Hi,

I have the following mathematical problem:

Given is a polynomial in x:

0 = sum_{i=0}^{N}  (-1)^i    a_i  x^i

The roots of this polynomial {x_1 .... x_N} are all real.

The question is:

Is there an unambiguous way to find a symmetric matrix B that has the
eigenvalues {x_1 ... x_N}, when the diagonal elements of B are known?

A related problem is:

Which unitary transformation  transforms the diagonal matrix X (with the

diagonal elements {x_1 ... x_N}) to a symmetric matrix B with known
diagonal elements?

Any help or hints what to look for is very much appreciated.

Thank you in advance.

Matthias

--
-----------------------------------------
G. Matthias Ullmann
Department of Molecular Biology
The Scripps Research Institute
10550 N. Torrey Pines Rd., TPC-15
La Jolla, CA 92037 USA

Phone:  858-784-8889
Fax:    858-784-8896
e-mail: [email-masked]
www:    http://www.scripps.edu/~ullmann