RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zh. Vychisl. Mat. Mat. Fiz.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1932 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 519.62

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
\Bibitem{Sha09} \by B.~Z.~Shavarovskii \paper Similarity transformations of decomposable matrix polynomials and related questions \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2009 \vol 49 \issue 9 \pages 1539--1553 \mathnet{http://mi.mathnet.ru/zvmmf4746} \zmath{https://zbmath.org/?q=an:05649694} \elib{http://elibrary.ru/item.asp?id=12901459} \transl \jour Comput. Math. Math. Phys. \yr 2009 \vol 49 \issue 9 \pages 1469--1482 \crossref{https://doi.org/10.1134/S0965542509090012} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000269917100001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350134018} 

• http://mi.mathnet.ru/eng/zvmmf4746
• http://mi.mathnet.ru/eng/zvmmf/v49/i9/p1539

 SHARE:

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
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
•  Number of views: This page: 369 Full text: 72 References: 31 First page: 10