复矩阵Hermitian部分的2~n次幂等性

针对J.Gross所研究的复矩阵A的Hermitian部分的幂等性问题,将其扩展到复矩阵A的Hermitian部分的2~n次幂等性,得到了复矩阵A的Hermitian部分是2~n次幂等的充分必要条件;同时也得到了复矩阵A的Hermitian部分是2~n次幂等与A的正规性和特征值之间的关系-由任意2个性质可以推出第3个性质.最后,J.Gross得到的结果成为本文的推论.

2~n Idempotency of the Hermitian part of a complex matrix

The problem for the 2~n idempotency of the Hermitian part of the complex matrix A was studied by J.Gross. In this paper, the problem before was developed to the idempotency of the Hermitian part of the complex matrix A. The sufficient and necessary condition for the 2~n idempotency of the Hermitian part of the complex matrix A is given; the relation among the 2~n idempotency of the hermitian part of the complex matrix A, the normality of A and the eigenvalues of the A was also given. It is that any one of them can be got by the others. Finally, the result of J.Gross can be directly got by the Theorem in this paper.