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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1539–1553 (Mi zvmmf4746)  

This article is cited in 2 scientific papers (total in 2 papers)

Similarity transformations of decomposable matrix polynomials and related questions

B. Z. Shavarovskii

Pidstryhach Institute for Applied Problems of Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. Nauchnaya 3-b, Lviv, 79601, Ukraine

Abstract: A elationship is found between the similarity transformations of decomposable matrix polynomials with relatively prime elementary divisors and the equivalence transformations of the corresponding matrices with scalar entries. Matrices with scalar entries are classified with respect to equivalence transformations based on direct sums of lower triangular almost Toeplitz matrices. This solves the similarity problem for a special class of finite matrix sets over the field of complex numbers. Eventually, this problem reduces to the one of special diagonal equivalence between matrices. Invariants of this equivalence are found.

Key words: matrix polynomial (polynomial matrix), similarity of matrix sets, invariants of matrix sets with respect to similarity, equivalence of matrices.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1469–1482

Bibliographic databases:

UDC: 519.62
Received: 17.09.2008

Citation: B. Z. Shavarovskii, “Similarity transformations of decomposable matrix polynomials and related questions”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1539–1553; Comput. Math. Math. Phys., 49:9 (2009), 1469–1482

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bazilevich Yu.N., “The Best Reduction of Matrices to Block-Triangular Form For Hierarchical Decomposition Problems”, Cybern. Syst. Anal., 53:3 (2017), 456–463  crossref  mathscinet  zmath  isi  scopus
    2. Shavarovskii B.Z., “Canonical Form of Reduced 3-By-3 Matrix With One Characteristic Root and With Some Zero Subdiagonal Elements”, J. Math., 2019, 7646132  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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