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To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications

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Abstract

For a q-parameter (q ≥ 2) polynomial matrix of full rank whose regular and singular spectra have no points in common, a method for computing its partial relative factorization into a product of two matrices with disjoint spectra is suggested. One of the factors is regular and is represented as a product of q matrices with disjoint spectra. The spectrum of each of the factors is independent of one of the parameters and forms in the space ℂq a cylindrical manifold w.r.t. this parameter. The method is applied to computing zeros of the minimal polynomial with the corresponding eigenvectors. An application of the method to computing a specific basis of the null-space of polynomial solutions of the matrix is considered. Bibliography: 4 titles.

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REFERENCES

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  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg

    V. N. Kublanovskaya

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  1. V. N. Kublanovskaya
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 296, 2003, pp. 89–107.

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Kublanovskaya, V.N. To solving multiparameter problems of algebra. 2. The method of partial relative factorization and its applications. J Math Sci 127, 2006–2015 (2005). https://doi.org/10.1007/s10958-005-0158-3

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  • DOI: https://doi.org/10.1007/s10958-005-0158-3

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