满足某些多项式恒等式的矩阵的表征

Characterization of Matrices Satisfying Certain Polynomial Identities

讨论两个问题 :a .证明满足条件 1 dHM(AX) =dHM(XA) , X∈Mn(C)的奇异矩阵A的表征可简化为满足条件 2 dHM(AX) =0 , X∈Mn(C)的矩阵A的表征 ;b .给出关于条件 2的表征的两个结果 .这里H是n次对称群Sn 的子群 ,而dHM

This paper deals with two problems: a. The characterization of the singular matrices A satisfying (1) d H M(AX)=d H M(XA),X∈M n(C) can be reduced to that of matrices satisfying (2) d H M(AX)= 0, X∈M(C); b. two results on the characterization of (2) are obtained. d H M denotes matrix function derived from unitary matrix representing M of the group H, S n shall be the symmetric group of degree n , and H denotes a subgroup of S n .