2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59951Let $M$ 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 PagesRings and AlgebrasAlgebraic Geometry15A29;47A75;14N05text