ELA, Volume 13, pp. 405-418, December 2005, abstract.

Schur Complements and Banachiewicz-Schur Forms

Yongge Tian and Yoshio Takane

Through the matrix rank method, this paper gives necessary 
and sufficient conditions for a partitioned matrix to have 
generalized inverses with Banachiewicz-Schur forms. In 
addition, this paper investigates the idempotency of 
generalized Schur complements in a partitioned idempotent 
matrix.