摘要
利用矩阵迹的性质,从矩阵相似性、半正定性、两个矩阵乘积、方幂运算、Kronecker积、矩阵函数eA的行列式等角度来刻画迹为零矩阵的一些性质,给出了这类矩阵的几个充分必要条件.根据迹为零矩阵的这些性质并利用矩阵的Jordan标准型,指出它在矩阵分解中的若干应用,最后得到迹为零矩阵AB-BA方幂的迹也为零的两个结论.
By using the characteristics of the matrix trace. We described the properties of the matrices with trace zero in terms of the simility of matrices, positive semidefinite matrices, the product of two matrices, the power of matrix, Kronecker product, the determinant of e^A, etc. Several sufficient and necessary conditions for a matrix to be a matrix with trace zero are put forward. Some applications in the matrix factorization of these matrices are given based on their properties and Jordan canonical form of them. Two conclusions that the trace of the power of matrix AB-BA is also equal to zero are presented in the end.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2008年第4期409-411,共3页
Journal of Shenyang Normal University:Natural Science Edition
关键词
矩阵的迹
相似矩阵
半正定矩阵
幂零矩阵
trace of a matrix
similarity matrices
positive semidefinite matrices
nilpotent matrix
