矩阵伪逆的一个等价定义及其应用

Equivalent Definitions of Pseudo-Inverse on Matrix and Its Applications

在Moore-Penrose逆的4个代数方程中两边取共轭转置,得到与之等价的定义。运用该等价定义,研究了矩阵A的自反广义逆、最小二乘广义逆、极小范数广义逆、M00re-Penrose逆,A{1,2,3}逆、A{1,2,4}逆及A{1,3,4}逆,得到了其间关系的若干充要条件。

Taking the conjugate transpose to four algebraic equations of the Moore-Penrose inverse,an equivalent definition of the Moore-Penrose inverse of matrix is gained.Futher,we study the reflexive generalized inverse,the least squares generalized inverse,the minimum norm generalized inverse,the Moore-Penrose inverse,A{ 1,2,3} inverse,A { 1,2,4} inverse and A { 1,3,4} inverse of matrix A,and obtain several necessary and sufficient conditions about their relationship.