Generalized inverses of partitioned matrices in Banachiewicz–Schur form

Jerzy K. Baksalary, George P.H. Styan
2002 Linear Algebra and its Applications  
The problem of developing conditions under which generalized inverses of a partitioned matrix can be expressed in the so-called Banachiewicz-Schur form is reconsidered. Theorem of Marsaglia and Styan [Sankhyā Ser. A 36 (1974) 437], concerning the class of all generalized inverses, the class of reflexive generalized inverses, and the Moore-Penrose inverse, is strengthened and new results are established for the classes of outer inverses, least-squares generalized inverses, and minimum norm generalized inverses.
doi:10.1016/s0024-3795(02)00334-8 fatcat:azpsi2qgjje5rc24pfwergzwfu