To solving multiparameter problems of algebra. 11. Computing the regular spectrum of a polynomial matrix

Abstract

For a general multiparameter polynomial matrix \(F(\bar \lambda )\), solution of the equation \(F(\bar \lambda )x = 0\) at points of the finite spectrum of \(F(\bar \lambda )\) is considered. Points of the spectrum of \(F(\bar \lambda )\) are classified in terms of solutions of the determinantal system of nonlinear algebraic equations and also in terms of zeros of certain scalar polynomials (in particular, the characteristic polynomial of the matrix). Algorithms for computing points of the finite regular spectrum of the matrix and the corresponding vectors are presented. Bibliography: 7 titles.