Computation of Characteristics of the Regular Finite Spectrum of a Singular Multiparameter Polynomial Matrix

A modification of a known algorithm for computing the generating eigenvectors of a multiparameter polynomial matrix of full column rank is presented. This modification permits one to compute the characteristic polynomial (or its divisors) of a singular matrix. The algorithm proposed can be extended to the general case and used for computing a minimal basis of the image of a polynomial matrix and also the greatest common divisors of scalar and matrix polynomials. An illustration of the algorithm performance is provided. Bibliography: 6 titles.