A Matrix Identity on the Schur Complement

Authors

Fuzhen Zhang, Nova Southeastern University; Shenyang Normal UniversityFollow

Document Type

Article

Publication Date

2004

Publication Title

Linear and Multilinear Algebra

Keywords

LDU factorization, Quotient formula, Schur complement

ISSN

0308-1087

Volume

52

Issue/No.

5

First Page

367

Last Page

373

Abstract

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

NSUWorks Citation

Zhang, Fuzhen, "A Matrix Identity on the Schur Complement" (2004). Mathematics Faculty Articles. 71.
https://nsuworks.nova.edu/math_facarticles/71

DOI

10.1080/03081080310001645172