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Journal of Mathematical Sciences

, Volume 182, Issue 6, pp 748–753 | Cite as

A criterion for unitary congruence between complex matrices

  • Yu. A. Al’pinEmail author
  • Kh. D. Ikramov
Article
  • 56 Downloads

Let A and B be square complex matrices of the same order n. Based on an important result Y. P. Hong and R. A. Horn, we propose a criterion for verifying unitary congruence of these matrices. The criterion requires that a finite number of arithmetic operations be performed. No criteria with this finiteness property were previously known. Bibliography: 7 titles.

Keywords

Finite Number Arithmetic Operation Complex Matrice Finiteness Property Unitary Congruence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1985).zbMATHGoogle Scholar
  2. 2.
    C. Pearcy, “A complete set of unitary invariants for operators generating finite W *-algebras of type I,” Pacif. J. Math., 12, 1405-1416 (1962).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Yu. A. Al’pin and Kh. D. Ikramov, “A criterion for unitary congruence between matrices,” Dokl. Ross. Akad. Nauk, 437, 7-8 (2011).MathSciNetGoogle Scholar
  4. 4.
    Y. P. Hong and R. A. Horn, “A characterization of unitary congruence,” Linear Multilinear Algebra, 25, 105-119 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Yu. A. Al’pin and Kh. D. Ikranov, “On unitary similarity of matrix families.” Mat. Zametki, 74, 815-826 (2003).Google Scholar
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    B.L. van der Waerden, Algebra, Vol. II, Springer (2003).Google Scholar
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    C. Pappacena, “An upper bound for the length of a finite-dimensional algebra,” J. Algebra, 197, 535-545 (1997).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Kazan’ State UniversityKazan’Russia
  2. 2.Moscow State UniversityMoscowRussia

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