【摘要】 研究了矩阵空间保不变量问题中的不变量是矩阵的逆的线性算子保持问题.去掉了域的特征限制,刻画了至少包含4个元素的任意域F上的全矩阵空间Mn(F)的保逆的可逆线性算子形式.利用保幂等的结论证明了f为Mn(F)上保持逆矩阵的可逆线性算子当且仅当存在P∈GLn(F),使得f(A)=εPAP-1,A∈Mn(F),ε=±1∈F;或者存在P∈GLn(F),使得f(A)=εPATP-1,A∈Mn(F),ε=±1∈F.更多还原

【Abstract】 One of the problems of invariance preservation on matrix space, preserving linear operator so that the invariant is matrix, is studied. Eliminating the restriction of the characteristic of field,the forms of invertible linear operator preserving inverses of matrices over full matrix space with at least four elements are described. Using the conclusions of idempotent-preserving, it is proved that f is the invertible linear operator from W-n（F） into M-n（F） preserving inverses of matrices, if and only if there exists P∈GL-n（F）, such that f（A）=εPA^TP^-1,A∈M-n（F）,ε=±1∈F,or there exists P∈GL-n（F）,such that f（A）=εAP^T,A∈M-n（F）,ε=±1∈F.更多还原