Elimination for Coefficients of Special Characteristic Polynomials

Abstract

Computing the relations for the coefficients satisfied by the characteristic polynomial of the Kronecker product of a general $n \times n$ matrix by a general $m \times m$ matrix leads to an elimination problem that is already difficult for small values of $n$ and $m$. In this article we focus on the problems for $(n, m) \in \{ (2,3), (2,4), (3,3)$ and use these problems for developing and testing a new elimination technique called elimination by degree steering.