The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

Details The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

2000-09-15

arxiv.org/abs/math/0009163v1

Mathematics

Rings and Algebras

9 Pages

Scientific paper

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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