Journal of Mathematical Sciences

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

Simultaneous reduction to block triangular form by a unitary congruence transformation

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Abstract

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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References

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    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
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    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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