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×n matrix by a general m × 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) ∈ {(2, 3), (2, 4), (3, 3)} and use these problems for developing and testing a new elimination technique called elimination by degree steering.

Keywords:

• Primary 14Q20, 68W30, 20C40, 13P10
• Secondary 14A05
• Characteristic polynomial
• Kronecker product
• elimination
• Janet bases