分块矩阵的广义迹及其应用

The Generalized Trace of Partitioned Matrix and Its Application

在矩阵论中,有许多学者对矩阵的迹,矩阵的广义迹及矩阵特殊运算的广义迹等进行了讨论和研究,而分块矩阵是矩阵领域中的重要内容之一,在许多方面都有着重要应用,但对分块矩阵的广义迹的讨论却未曾涉及,通过矩阵的广义迹的启发,得出了分块矩阵的广义迹的计算方法,并用此方法计算了矩阵的广义Hadamard积的广义迹.

In matrix theory,the trace of matrix,the generalized trace of the matrix and the genralized trace of thematrix special operation are discussed and researched by many scholars. Partitioned matrix is one of the importantcontent in the field of matrix,which has important application in many ways,but for the generzlized trace of thepartitioned matrix have been not discussed. Through the enlightenment of the generalized trace of the matrix,thecalculative method of the generalized trace of the partitioned matrix is obtained,which is used to calculate thegeneralized trace of the generalized Hadamard product of the matrix.