Rank equalities related to outer inverses of matrices and applications

• Published in: Linear & multilinear algebra Vol. 49; no. 4; pp. 269 - 288
• Main Author: Tian, Yongge
• Format: Journal Article
• Language: English
• Published: Gordon and Breach Science Publishers 15.12.2001
• Subjects: AMS Subject Classifications:15A03, 15A09; Drazin inverse; Moore-Penrose inverse; Outer inverse; Rank; Weighted Moore-Penrose inverse

A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin invers...