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Mat. Zametki, 2000, Volume 68, Issue 5, Pages 648–652 (Mi mz986)  

This article is cited in 7 scientific papers (total in 7 papers)

On the Simultaneous Triangulability of Matrices

Yu. A. Alpin, N. A. Koreshkov

Kazan State University

Abstract: Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion, classical theorems from Lie algebra theory are used, and known sufficient conditions of triangulability are also given a natural interpretation in terms of this theory. The other criterion is discussed in the framework of the associative algebras. Here the decisive fact is the Wedderburn theorem on the nilpotence of a finite-dimensional nilalgebra.

DOI: https://doi.org/10.4213/mzm986

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English version:
Mathematical Notes, 2000, 68:5, 552–555

Bibliographic databases:

UDC: 519.6
Received: 04.11.1999

Citation: Yu. A. Alpin, N. A. Koreshkov, “On the Simultaneous Triangulability of Matrices”, Mat. Zametki, 68:5 (2000), 648–652; Math. Notes, 68:5 (2000), 552–555

Citation in format AMSBIB
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\by Yu.~A.~Alpin, N.~A.~Koreshkov
\paper On the Simultaneous Triangulability of Matrices
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 5
\pages 648--652
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835447}
\zmath{https://zbmath.org/?q=an:0993.15012}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 5
\pages 552--555
\crossref{https://doi.org/10.1023/A:1026659205382}
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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. Bourgeois G., “Pairs of Matrices, One of Which Commutes with their Commutator”, Electron. J. Linear Algebra, 22 (2011), 593–597  crossref  mathscinet  zmath  isi  elib
    2. M. V. Mulyukov, “Ob ustoichivosti nekotorykh differentsialnykh sistem s zapazdyvaniem”, Izv. IMI UdGU, 2012, no. 1(39), 97–98  mathnet
    3. A. N. Abyzov, Yu. A. Alpin, N. A. Koreshkov, M. F. Nasrutdinov, S. N. Tronin, “Algebraicheskie issledovaniya v Kazanskom universitete ot V. V. Morozova do nashikh dnei”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 44–59  mathnet
    4. M. V. Mulyukov, “On factorization of the characteristic quasipolynomial of a system of linear differential equations with delay”, Russian Math. (Iz. VUZ), 57:9 (2013), 31–36  mathnet  crossref
    5. Bourgeois G., “Common Invariant Subspace and Commuting Matrices”, Linear Alg. Appl., 438:7 (2013), 3030–3038  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Baker Ch.T.H., “Observations on Evolutionary Models with (Or Without) Time Lag, and on Problematical Paradigms”, Math. Comput. Simul., 96:SI (2014), 4–53  crossref  mathscinet  isi  scopus  scopus
    7. Grosjean N., Huillet T., Rollet G., “On discrete evolutionary dynamics driven by quadratic interactions”, Theory Biosci., 135:4 (2016), 187–200  crossref  mathscinet  isi  elib  scopus
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