反对称矩阵空间行列式保持映射

Linear maps preserving determinant on skew-symmetric matrices

令SKn(R)为实数域R上所有n×n反对称矩阵构成的空间,研究SKn(R)上行列式的保持映射.并且当满足下列情况之一时,对它进行了刻画.1. det(A+λB)=det((A)+λ(B) ) A,B∈SKn(R) λ∈R2. 是满射且对两个特殊的λ有det(A+λB)=det((A)+λ(B) ) A,B∈SKn(R)3. 是加法映射且detA=det((A) ) A∈SKn(R)

Let SK_n(R) be the space of all n×n kew-symmetric matrices over the field, R, of all real numbers. the maps  preserving determinant on SK_n(R) are studied.  is completely characterized when it satisfies one of the following conditions: 1. det(A+λB)=det((A)+λ(B)) for all A,B in SK_n(R) and λ in R. 2.  is surjective and det(A+λB)=det((A)+λ(B)) for all A, B in SK_n(R) and two specific λ in R. 3.  is additive and detA=det((A)) for all A in SK_n(R).