Journal of Mathematical Sciences

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

Simultaneous reduction to block triangular form by a unitary congruence transformation

  • Kh. D. IkramovEmail author
  • H. Fassbender


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.


Russia Computational Mathematic Symmetric Matrice Hermitian Matrice Classical Theorem 
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  1. 1.
    M. Marcus and H. Mink, A Survey of Matrix Theory and Matrix Inequalities, Allyn and Bacon, Boston (1964).zbMATHGoogle Scholar
  2. 2.
    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).zbMATHCrossRefMathSciNetGoogle 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).zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1985).zbMATHGoogle Scholar
  5. 5.
    D. C. Youla, “A normal form for a matrix under the unitary congruence group,” Canad. J. Math., 13, 694–704 (1961).zbMATHMathSciNetGoogle 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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