The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

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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.
9 Pages

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Rings and Algebras, Algebraic Geometry, 15A29;47A75;14N05

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http://salesiana.dossiersoluciones.com/handle/123456789/59951

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0009163
 http://arxiv.org/abs/math/0009163

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arXiv