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Selfadjoint Endomorphisms

  • Jonathan S. Golan

Abstract

Selfadjoint endomorphisms of inner product spaces are defined and studied. Any selfadjoint endomorphism of a finitely-generated inner product space is shown to have a nonempty spectrum. The notion of orthogonal decomposition of an endomorphism is introduced. Selfadjoint endomorphisms of finitely-generated inner product spaces are shown to be orthogonally diagonalizable, with the converse true for spaces over the real numbers. Positive-definite endomorphisms are introduced and characterized. Application is made to Cholesky decompositions. Isometries of finitely-generated inner product spaces are studied and characterized.

Keywords

Product Space Diagonal Entry Symmetric Matrice Hermitian Matrix Hermitian Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of HaifaHaifaIsrael

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