Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications
Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications
A complex matrix X is called an $\{i,\ldots, j\}$ -inverse of the complex matrix A, denoted by $A^{(i,\ldots, j)}$ , if it satisfies the ith, …, jth equations of the four matrix equations (i) $AXA = A$ , (ii) $XAX=X$ , (iii) $(AX)^{*} = AX$ , (iv) $(XA)^{*} = XA$ …