Inverses of \(2\times 2\) block matrices
type: Item
instance of: scholarly article
title: Inverses of \(2\times 2\) block matrices
zbMATH Open document ID: 1001.15002
DOI: 10.1016/S0898-1221(01)00278-4
author: Tzon-Tzer Lu
author: Sheng-Hua Shiou
publication date: 2002-08-15T00:00:00Z
review text: Explicit inverse formulas for \(2\times 2\) block matrices with three different partitions are derived. A complete treatment is given. The results are used to get inverses of \(2\times 2\) block triangular matrices. The main theorems are also applied to structured matrices including bisymmetric, Hamiltonian, Hankel, Toeplitz, circulant, Hermitian, centro-Hermitian, and their skew Hermitian matrices. The completion problem of a \(2\times 2\) block matrix and its inverse is discussed.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 1781464
zbMATH Keywords: explicit inverse
zbMATH Keywords: bisymmetric matrix
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: Hankel matrix
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: circulant matrix
zbMATH Keywords: centro-Hermitian matrix
zbMATH Keywords: skew-Hermitian matrix
zbMATH Keywords: block matrices
zbMATH Keywords: triangular matrices
zbMATH Keywords: structured matrices
zbMATH Keywords: completion problem
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1781464