Abstract:
A certain standard form is found for a complex matrix with respect to equivalent transformations by quasi-diagonal matrices. The solvability of certain matrix equations in the rings of quasi-diagonal matrices is examined using this standard form.
Key words:
matrix equation, quasi-diagonal solution to matrix equations, reduction of a matrix to its standard form, similarity of matrix polynomials.
Citation:
B. Z. Shavarovskii, “Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1353–1362; Comput. Math. Math. Phys., 46:8 (2006), 1283–1292
\Bibitem{Sha06}
\by B.~Z.~Shavarovskii
\paper Solvability of matrix equations in rings of quasi-diagonal matrices and similarity of matrix polynomials
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1353--1362
\mathnet{http://mi.mathnet.ru/zvmmf423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2287355}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1283--1292
\crossref{https://doi.org/10.1134/S0965542506080021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748331253}
Linking options:
https://www.mathnet.ru/eng/zvmmf423
https://www.mathnet.ru/eng/zvmmf/v46/i8/p1353
This publication is cited in the following 1 articles:
B. Z. Shavarovskii, “Similarity transformations of decomposable matrix polynomials and related questions”, Comput. Math. Math. Phys., 49:9 (2009), 1469–1482
Citation in format AMSBIB
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