Elimination for coefficients of special characteristic polynomials. (English) Zbl 1169.14324
Summary: 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.
MSC:
14Q20 | Effectivity, complexity and computational aspects of algebraic geometry |
68W30 | Symbolic computation and algebraic computation |
20C40 | Computational methods (representations of groups) (MSC2010) |
13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
14A05 | Relevant commutative algebra |