Journal of Mathematical Sciences

, Volume 224, Issue 6, pp 877–882 | Cite as

The Congruent Centralizer of a Block Diagonal Matrix

  • Kh. D. Ikramov

Let a complex matrix A be the direct sum of its square submatrices B and C that have no common eigenvalues. Then every matrix X belonging to the centralizer of A has the same block diagonal form as the matrix A. This paper discusses how the conditions on the submatrices B and C should be modified for an analogous assertion about the congruent centralizer of A, which is the set of matrices X such that X * AX = A, to be valid. Also the question whether the matrices in the congruent centralizer are block diagonal if A is a block anti-diagonal matrix is considered. Bibliography: 2 titles.


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  1. 1.
    R. A. Horn and C. R. Johnson, Matrix Analysis. Second edition, Cambridge University Press, Cambridge (2013).MATHGoogle Scholar
  2. 2.
    D. Kressner, C. Schröder, and D. S. Watkins, “Implicit QR algorithms for palindromic and even eigenvalue problems,” Numer. Algorithms, 51, 209–238 (2009).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Moscow Lomonosov State UniversityMoscowRussia

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