科研之友
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摘要
Let C be the field of all complex numbers, M-n the space of all n x n matrices over C, and S-n the subspace of M-n consisting of all symmetric matrices. The map phi : S-n -> M-n satisfies that A - lambda B is k-potent in S-n implying that phi(A) - lambda phi (B) is k-potent in M-n, where lambda epsilon C, then there exist an invertible matrix P epsilon M-n and epsilon epsilon C with epsilon(k) = epsilon such that phi(X) = epsilon P-1 (X) P for every X epsilon S-n. Moreover, the inductive method used in this paper can be used to characterise similar maps from M-n to M-n.
