A characterization of the Moore-Penrose inverse
The inverse \(X\) of a square matrix \(A\) may be characterized as the unique matrix for which the two by two block matrix with entries \(\{A,I,I,X\}\) has the same rank as \(A\). This paper gives a generalization for singular and rectangular \(A\) using the Moore-Penrose inverse \(A^ +\).
scientific article; zbMATH DE number 166251