矩阵Moore—Penrose逆中子矩阵秩的计算公式

首先引入了M~+中子矩阵E_1,E_2,E_3和E_4秩的一组计算公式,并给出了它们在各种常见条件下的简化形式,又推出了M~+中子矩阵的秩所满足的若干不等式;最后给出了复矩阵N=A+iB的Moore-Penrose逆N~+=C+iD中C,D秩的计算公式及若干不等式。

Calculating Formulas for Ranks of Submatrices of the Moore-Penrose Inverse

First,we introduce a set of formulas for calculating the ranks of Submatrices E1,E2,E3 and E4 in M+,and give a lot of reduced forms for these formulas under some general conditions.Then,we introduce some inequalities for ranks of submatrices in M and M +.Finally,we give a set of calculating formulas and some inequalities for ranks of matrices C and D in the Moore-Penrose inverse