From chemistry-request@server.ccl.net Tue Feb 29 14:36:36 2000 Received: from relay1.scripps.edu (relay1.scripps.edu [137.131.200.29]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id OAA29107 for ; Tue, 29 Feb 2000 14:36:35 -0500 Received: from hermes.scripps.edu (hermes.scripps.edu [137.131.200.6]) by relay1.scripps.edu (8.9.3/TSRI-3.1.0r) with ESMTP id LAA11220 for ; Tue, 29 Feb 2000 11:34:01 -0800 (PST) Received: from scripps.edu (bohr [137.131.252.68]) by hermes.scripps.edu (8.9.2/TSRI-3.0h) with ESMTP id LAA17144; Tue, 29 Feb 2000 11:33:58 -0800 (PST) Sender: ullmann@scripps.edu Message-ID: <38BC1F3F.F67CDBED@scripps.edu> Date: Tue, 29 Feb 2000 11:34:23 -0800 From: "G. Matthias Ullmann" X-Mailer: Mozilla 4.61 [en] (X11; U; Linux 2.0.36 i686) X-Accept-Language: en MIME-Version: 1.0 To: chemistry@ccl.net Subject: Math Problem: Polynomials and Matrices Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit 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: ullmann@scripps.edu www: http://www.scripps.edu/~ullmann