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Inverse-preserving Linear Maps Between Spaces of Matrices over Fields 被引量:3
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作者 Xian ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第3期873-878,共6页
Suppose F is a field different from F2, the field with two elements. Let Mn(F) and Sn(F) be the space of n × n full matrices and the space of n ×n symmetric matrices over F, respectively. For any G1, G2 ... Suppose F is a field different from F2, the field with two elements. Let Mn(F) and Sn(F) be the space of n × n full matrices and the space of n ×n symmetric matrices over F, respectively. For any G1, G2 ∈ {Sn(F), Mn(F)}, we say that a linear map f from G1 to G2 is inverse-preserving if f(X)^-1 = f(X^-1) for every invertible X ∈ G1. Let L (G1, G2) denote the set of all inverse-preserving linear maps from G1 to G2. In this paper the sets .L(Sn(F),Mn(F)), L(Sn(F),Sn(F)), L (Mn(F),Mn(F)) and L(Mn (F), Sn (F)) are characterized. 展开更多
关键词 Field Inverse-preserving linear map space of full matrices space of symmetric matrices
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