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Reduction of matrix polynomials to a special quasitriangular form

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Abstract

We find necessary and sufficient conditions for polynomials with matrix coefficients over an arbitrary field to be reducible via a similarity transformation to block triangular form with regular diagonal blocks of maximum degree.

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Literature Cited

  1. F. R. Gantmakher,Theory of Matrices, Chelsea, New York (1959).

    Google Scholar 

  2. P. S. Kazimirs'kii and L. M. Griniv, “Reduction of a regular matrix polynomial to quasitriangular form,”Dop. Akad. Nauk UkrRSR, Ser. A. No. 11, 973–975 (1972).

    MathSciNet  Google Scholar 

  3. P. S. Kazimirs'kii and L. M. Griniv, “Identification of a ‘large’ factor of a matrix polynomial,”Dop. Akad. Nauk UkrRSR, Ser. A, No. 4, 293–297 (1974).

    MathSciNet  Google Scholar 

  4. P. S. Kazimirskii and L. M. Gryniv, “Reduction of a regular matrix polynomial to quasidiagonal form,”Ukr. Mat. Zh.,26, No. 3, 318–327 (1974).

    MathSciNet  Google Scholar 

  5. P. S. Kazimirs'kii,Decomposition of Matrix Polynomials into Factors [in Ukrainian], Naukova Dumka, Kiev (1981).

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  6. B. Z. Shavarovs'kii, “On the reduction of matrix polynomials to block-triangular and block-diagonal forms,” in:Proceedings of the 10th Conference of Young Scholars of the Ukrainian Academy of Sciences Institute for Applied Problems of Mechanics and Mathematics [in Russian], L'vov (1984), Chpt. 2, pp. 225–228.

  7. B. Z. Shavarovs'kii, “Reduction of monic polynomial matrices with pairwise relatively prime elementary divisors to block-diagonal form,”Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1, 30–32 (1983).

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Authors
  1. B. Z. Shavarovs'kii
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Additional information

Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.

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Shavarovs'kii, B.Z. Reduction of matrix polynomials to a special quasitriangular form. J Math Sci 81, 3013–3019 (1996). https://doi.org/10.1007/BF02362585

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  • DOI: https://doi.org/10.1007/BF02362585

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