矩阵的等价标准形及其应用

Some applications of the equivalent standard form of matrix

矩阵的等价关系是矩阵理论中最基本的一个概念。本文利用矩阵的等价标准形,给出矩阵的满秩分解及Cylv asten定律的证明;并从矩阵的等价标准形出发,由浅入深地论述了矩阵的广义逆.

The equivalence relation of matrix is a most fundamental definition in matrix theory.In this paper,we give the decomposition theorem of full rank matrix and the proof of CYLVASTER law,and discuss the generalized inverse matrix from the equivalent standard form of matrix.