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.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 482, 2019, pp. 259–271.
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Khazanov, V.B. Computation of Characteristics of the Regular Finite Spectrum of a Singular Multiparameter Polynomial Matrix. J Math Sci 249, 281–289 (2020). https://doi.org/10.1007/s10958-020-04942-7
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DOI: https://doi.org/10.1007/s10958-020-04942-7