A Matrix Identity on the Schur Complement
Linear and Multilinear Algebra
LDU factorization, Quotient formula, Schur complement
This article presents a matrix identity on the Schur complement along with various applications. In particular, it gives a simple and transparent proof for the Crabtree–Haynsworth quotient formula for the Schur complement. Although its proof is straightforward, the identity yields a number of important results that appear to be unrelated
Zhang, Fuzhen, "A Matrix Identity on the Schur Complement" (2004). Mathematics Faculty Articles. 71.