Expressions for the Moore–Penrose inverse of block matrices involving the Schur complement

We present a formula for the Moore–Penrose inverse of a matrix of the form M=XNY, where X and Y are nonsingular. Based on this result, we develop explicit expressions for the Moore–Penrose inverse of a 2×2 complex block matrix M. We recover the cases when a Schur complement in M is either equal to z...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2015-04, Vol.471, p.353-368
Main Authors: Castro-González, N., Martínez-Serrano, M.F., Robles, J.
Format: Article
Language:English
Subjects:
Block matrix
Bordered matrix
Moore–Penrose inverse
Schur complement
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a formula for the Moore–Penrose inverse of a matrix of the form M=XNY, where X and Y are nonsingular. Based on this result, we develop explicit expressions for the Moore–Penrose inverse of a 2×2 complex block matrix M. We recover the cases when a Schur complement in M is either equal to zero or nonsingular. Some applications to banded matrices and bordered matrices are indicated.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2015.01.003