## Abstract

Letr Σ_{n}(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 : Σ_{n}(C) -> Σ_{n} (C) satisfying for any fixed irre- ducible characters X, X' -S_{C} the condition d_{x}(A +aB) = d_{χ}·(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 Σ_{И}(С).

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