Journal of Mathematical Sciences

, Volume 150, Issue 2, pp 1943–1950 | Cite as

Simultaneous reduction to block triangular form by a unitary congruence transformation



Analogs of some classical theorems on commuting matrices are proved. The new theorems deal with unitary congruences rather than unitary similarities; commutation is replaced by concommutation, defined in the paper, whereas normal and Hermitian matrices are replaced by conjugate-normal and symmetric matrices, respectively. Bibliography: 5 titles.


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  1. 1.
    M. Marcus and H. Mink, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston (1964).MATHGoogle Scholar
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    Y. P. Hong and R. A. Horn, “On simulataneous reduction of families of matrices to triangular or diagonal form by unitary congruences,” Linear Multilinear Algebra, 17, 271–288 (1985).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    H. Fassbender and Kh. D. Ikramov, “Some observations on the Youla form and conjugate-normal matrices,” Linear Algebra Appl., 422, 29–38 (2007).MATHCrossRefMathSciNetGoogle Scholar
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    R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1985).MATHGoogle Scholar
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    D. C. Youla, “A normal form for a matrix under the unitary congruence group,” Canad. J. Math., 13, 694–704 (1961).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Institute of Computational MathematicsTU BraunschweigGermany

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