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Special Matrices

Editor-in-Chief: da Fonseca, Carlos Martins


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2300-7451
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Immanant Conversion on Symmetric Matrices

M. Purificação Coelho
  • Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Bloco C6, Piso 2, Campo Grande, 1700-016 Lisboa, Portugal
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/ M. Antónia Duffner
  • Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Bloco C6, Piso 2, Campo Grande, 1700-016 Lisboa, Portugal
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/ Alexander E. Guterman
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  • Department of Higher Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119991, Russia
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Published Online: 2014-02-12 | DOI: https://doi.org/10.2478/spma-2014-0001

Abstract

Letr Σn(C) denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C) -> Σn (C) satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB) = dχ·(Φ(Α ) + αΦ(Β)) for all matrices A,В ε Σ„(С) and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С).

Keywords: Determinant; permanent; immanant; preservers; converters; symmetric matrices

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About the article

Received: 2013-08-29

Accepted: 2014-01-03

Published Online: 2014-02-12

Published in Print: 2014-01-01


Citation Information: Special Matrices, Volume 2, Issue 1, ISSN (Online) 2300-7451, DOI: https://doi.org/10.2478/spma-2014-0001.

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©2014 Alexander E. Guterman et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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