满足某些多项式恒等式的矩阵的表征  

Characterization of Matrices Satisfying Certain Polynomial Identities

作　　者：王心介[1] 

机构地区：[1]华中科技大学数学系

出　　处：《华中科技大学学报（自然科学版）》2001年第12期104-106,共3页Journal of Huazhong University of Science and Technology(Natural Science Edition)

摘　　要：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dHMThis 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 .

关 键 词：矩阵论 酉表示 陪集 轨道 奇异矩阵 矩阵函数 多项式恒等式 矩阵表征 

分 类 号：O151.21[理学—数学]