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

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.


Finite Number Arithmetic Operation Complex Matrice Finiteness Property Unitary Congruence 
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    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
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    Y. P. Hong and R. A. Horn, “A characterization of unitary congruence,” Linear Multilinear Algebra, 25, 105-119 (1989).MathSciNetzbMATHCrossRefGoogle Scholar
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    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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    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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