次迹为零的矩阵及其性质

Matrix with Zero Subtrace and Its Properties

给出次迹为零的矩阵的概念,从矩阵的次相似、次半正定、Kronecker与Hadamard积、矩阵函数等角度来刻画次迹为零的矩阵的一些性质,给出了这类矩阵的几个必要条件,并讨论它在矩阵分解中的应用.

In this paper,the concept of a matrix with zero subtrace is given,the properties of the matrix with zero subtrace are described in terms of the sub-similarity of the matrix,positive sub-semidefinite matrix,Kronecker pruduct,Hadamard pruduct,function of matrix,etc and several necessary conditions for this class of matrices are put forward.Some applications in the matrix factorization of these matrices are discussed.