Inverse-preserving Linear Maps Between Spaces of Matrices over Fields

作者：Xian; ZHANG反转保存线性图全矩阵空间相称性矩阵空间域可逆转性

摘要：Suppose F is a field different from F_2,the field with two elements.Let M_n(F) and S_n(F)bethe space of n×n full matrices and the space of n×n symmetric matrices over F,respectively.For anyG_1,G_2 ∈{S_n(F),M_n(F)},we say that a linear map f from G_1 to G_2 is inverse-preserving if f(X)~(-1)=f(X_(-1))for every invertible X ∈ G_1.Let (G_1,G_2)denote the set of all inverse-preserving linear mapsfrom G_1 to G_2.In this paper the sets (S_n(F),M_n(F)),(S_n(F),S_n(F)),(M_n(F),M_n,(F))and(M_n(F),S_n(F))are characterized.

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