Computing {2,4} and {2,3}-inverses using SVD and SVD like factorizations

Abstract

We derive conditions for the existence and investigate representations of {2, 4}and {2, 3}-inverses with prescribed range T and null space S. A general computational algorithm for {2,4} and {2,3} generalized inverses with given rank and prescribed range and null space is derived. The algorithm is derived generating the full-rank representations of these generalized inverses by means of various complete orthogonal matrix factorizations. More precisely, computational algorithm for {2,4}and {2,3}-inverses of a given matrix A is defined using an unique approach on SVD, QR and URV matrix decompositions of appropriately selected matrix W.