矩阵的一类特殊乘积及其广义行列式性质

A Special Multiplication of Matrices and Its Property of Generalized Determinant

本文受文献[1]的启发,定义了方阵和矩阵之间的一类特殊的乘积,即方阵左乘到矩阵中的若干行或右乘到矩阵中的若干列。利用[1]中的定理1,证明了这种乘积的广义行列式所满足的一个等式。利用这个等式,给出Liouville公式的一个推广。

In spired by literature[1],a special multiplication between a square matrix and a matrix is defined, i.e., to multiply somecolumns of the matrix from left, or to multiply some rows of thematrix from right, by the square matrix. By Theorem 1 in litera-ture [1], an identity satisfied by the generalized determinant of this mu-ltiplication is proved. Using this identity, Liouville formula is generalized.