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The multiplicative inverse eigenvalue problem over an algebraically closed field


Rosenthal, J; Wang, X (2001). The multiplicative inverse eigenvalue problem over an algebraically closed field. SIAM Journal on Matrix Analysis and Applications, 23(2):517-523.

Abstract

Let M be an n × n square matrix and let $p(\lambda)$ be a monic polynomial of degree n. Let $\mathcal{Z}$ be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix $Z\in\mathcal{Z}$ such that the product matrix MZ has characteristic polynomial $p(\lambda)$.
In this paper we provide new necessary and sufficient conditions when $\mathcal{Z}$ is an affine variety over an algebraically closed field.
©2001 Society for Industrial and Applied Mathematics

Abstract

Let M be an n × n square matrix and let $p(\lambda)$ be a monic polynomial of degree n. Let $\mathcal{Z}$ be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix $Z\in\mathcal{Z}$ such that the product matrix MZ has characteristic polynomial $p(\lambda)$.
In this paper we provide new necessary and sufficient conditions when $\mathcal{Z}$ is an affine variety over an algebraically closed field.
©2001 Society for Industrial and Applied Mathematics

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:eigenvalue completion, inverse eigenvalue problems, dominant morphism theorem
Language:English
Date:2001
Deposited On:11 Mar 2010 14:23
Last Modified:06 Dec 2017 20:53
Publisher:Society for Industrial and Applied Mathematics (SIAM)
ISSN:0895-4798
Additional Information:Copyright © 2001, Society for Industrial and Applied Mathematics
Publisher DOI:https://doi.org/10.1137/S0895479800378192

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