Journal of Mathematical Sciences

, Volume 182, Issue 6, pp 782–784 | Cite as

Products of orthoprojectors and Hermitian matrices


A proof of the following result is presented: A matrix AM n (C) can be represented as a product A = PH, where P is an orthoprojector and H is a Hermitian matrix, if and only if A satisfies the equation A *2 A = A * A 2 (the Radjavi-Williams theorem). Unlike the original proof, the new one makes no use of the Crimmins theorem. Bibliography: 2 titles.


Hermitian Matrix Hermitian Matrice Original Proof 


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  1. 1.
    H. Radjavi and J. P. Williams, “Products of self-adjoint operators,” Michigan Math. J. 16, 177–185 (1969).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    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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