A simplified proof of a theorem on the difference of the moore–penrose inverses of two positive semi–difinte matrices

Abstract

Simplified proofs are given of a standard result that establishes positive semi–definiteness of the difference of the inverses of two non–singular matrices, and of the extension of this result by Milliken and Akdeniz (1977) to the difference of the Moore–Penrose inverse of two singular matrices.

Keywords:

• generalized inverse
• Moore–Penrose inverse
• Positive semi–definite matrix