Lavoie inequalities for weighted generalized inverses of matrices

Abstract

Work on Lavoie inequalities in the past was done mainly on Moore–Penrose inverse and {1, 4}-inverses of matrices. To our best knowledge, there was no work published on generalized inverses of matrices based on {2}-inverses and weighted generalized inverses. In this article, we present the Lavoie inequalities for weighted {2, 4}-inverses and weighted Moore–Penrose inverse of matrices. Moreover, the Lavoie inequalities for {2, 4}-inverses of matrices are also obtained as special cases.