分块矩阵Moore－Penrose广义逆的一个表达式

An Explicit Formula for the Moore-penrose Generalized Inverse of a Partitioned Matrix

给出了按列或按行分块的矩阵Ｍｏｏｒｅ－ｐｅｎｒｏｓｅ广义逆的一个公式及其基于Ｐｅｎｒｏｓｅ方程组的直接证明，对一些重要特例作了推论。证明中给出的有关引理还包含了关于Ｍ一Ｐ逆阵及正交投影阵的若干有用性质。

An explicit formula was given for the Moore-Penrose generalized inverse of amatrix being partitioned by columns or by rows with its proof directly based on Penrose'S equations. Corollaries were obtained for some important special cases. Several useful properties of M-P inveise of matrix and the orthogonal projection matrix were included in some of the lemmas given in the proof.