Existence Criteria and Related Relation of the gMP Inverse of Matrices

Abstract

New characterizations of the gMP inverse are provided by the core part of the core-EP decomposition. We also answer the question as to whether X is the gMP inverse of A under the conditions of R(X)⊆R(A*Ak) or N((Ak)*)⊆N(X). We investigate the relationship between the core-EP inverse and the gMP inverse.Using the gMP inverse, the gMP relation is investigated in view of the core-EP decomposition.

Keywords

• gMP inverse
• core-EP inverse
• Moore–Penrose inverse
• index