Immanant Conversion on Symmetric Matrices
M. Purificação Coelho ; M. Antónia Duffner ; Alexander E. Guterman
Special Matrices, Tome 2 (2014), / Harvested from The Polish Digital Mathematics Library
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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).

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267527 
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     author = {M. Purifica\c c\~ao Coelho and M. Ant\'onia Duffner and Alexander E. Guterman},
     title = {Immanant Conversion on Symmetric Matrices},
     journal = {Special Matrices},
     volume = {2},
     year = {2014},
     zbl = {1294.15008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0001}
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M. Purificação Coelho; M. Antónia Duffner; Alexander E. Guterman. Immanant Conversion on Symmetric Matrices. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0001/

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