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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