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Journal of Mathematical Sciences

, Volume 182, Issue 6, pp 787–792 | Cite as

Products of orthoprojectors and a Theorem of Crimmins

  • Kh. D. Ikramov
Article
  • 37 Downloads

A proof of the following result, due to T. Crimmins, is proposed: A matrix AM n (C) can be represented as a product of orthoprojectors P and Q if and only if A satisfies the equation A 2 = AA*A. Bibliography: 3 titles.

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References

  1. 1.
    G. Corach and A. Maestripieri, “Products of orthogonal projections and polar decompositions,” Linear Algebra Appl., 434, 1594–1609 (2011).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    H. Radjavi and J. P. Williams, “Products of self-adjoint operators,” Michigan Math. J., 16, 177–185 (1969).MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Y. P. Hong and R. A. Horn, “The Jordan canonical form of a product of a Hermitian and a positive semidefinite matrix,” Linear Algebra Appl., 147, 373–386 (1991).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia

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