Journal of Mathematical Sciences

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

Products of orthoprojectors and a Theorem of Crimmins

  • Kh. D. Ikramov

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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  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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