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The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

Joachim Rosenthal·Xiaochang Wang
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Abstract

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

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Joachim Rosenthal, Xiaochang Wang. 2000-09-15. The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field. https://arxiv.org/abs/math/0009163

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