代数闭域上的乘性本征值问题
The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field
摘要：
令$M$是方阵，令$p(t)$是$n$次的一元多项式。令$Z$是$n\times n$矩阵的集合。乘法逆本征值问题要求在$Z$中构造一个矩阵，使得乘积矩阵$MZ$具有特征多项式$p(t)$。本文给出了$Z$是代数闭域上仿射簇的新的充要条件。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
