Abstract
We study the problem of the decomposition of a matrix polynomial over an arbitrary field into a product of factors of lower degrees with preassigned characteristic polynomials. We find necessary conditions for the existence of the required factorization, which are also sufficient for certain classes of matrix polynomials. The proposed method makes it possible to solve the problem completely for matrix polynomials with one nonconstant invariant factor.
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Literature Cited
P. S. Kazimirs'kii,Decomposition of Matrix Polynomials into Factors [in Ukrainian], Naukova Dumka, Kiev (1981).
P. S. Kazimirs'kii, “On the decomposition of a polynomial matrix into linear factors,”Visn. L'viv. Politekhn. Inst.: Certain questions of the theory of differential equations and algebra [in Ukrainian], No. 8, 53–60 (1965).
P. S. Kazimirskii, “The necessity of conditions for decomposability of a matrix polynomial into linear factors,”Ukr. Mat. Zh.,29, No. 5, 657–661 (1977).
V. M. Petrichkovich and V. M. Prokip, “On the factorization of polynomial matrices over an arbitrary field,”Ukr. Mat. Zh.,38, No. 4, 478–483.
V. M. Prokip, “On the uniqueness of a monic factor of a matrix polynomial over an arbitrary field,”Ukr. Mat. Zh.,45, No. 6, 803–808 (1993).
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Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.
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Prokip, V.M. Parallel factorizations of matrix polynomials over an arbitrary field. J Math Sci 81, 3020–3023 (1996). https://doi.org/10.1007/BF02362586
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DOI: https://doi.org/10.1007/BF02362586