特殊矩阵的Kronecker积  

Kronecker Product of Special Matrices

作　　者：杜鹃[1] 范啸涛[1] 冯思臣[1] 

机构地区：[1]成都理工大学信息管理学院,四川成都610059

出　　处：《四川师范大学学报（自然科学版）》2009年第1期56-59,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10471112)资助项目

摘　　要：在已有的Kronecker积性质的基础上给出了正规矩阵、对角矩阵、Hermite矩阵、相合矩阵、非负矩阵、M-矩阵、正定矩阵、半正定矩阵等特殊矩阵的kronecker积的性质,还得到了Kronecker积的奇异值分解的运算方法.另外,证明了Kronecker积的指数矩阵函数的运算性质与乘积矩阵的Kronecker积幂的运算性质;最后还推出了kronecker积的微分运算法则.Based on the well-known properties of the Kronecker product, some other properties of Kronecker product of some special matrices are discussed in this paper, such as normal, diagonal, Hermite, congruent, nonnegative, positive definite, semi-positive definite and M-matrices, etc. The singular value decomposition operation of the Kronecker product is given. Moreover, the operative properties of exponential matrix function of the Kronecker product and the operative properties of the Kronecker power for productive matrices are also proved. And finally, the differential operation rules of the Kronecker product are also obtained.

关 键 词：矩阵 直积 KRONECKER积 

分 类 号：O151.21[理学—数学]