Completing a symmetric \(2\times 2\) block matrix and its inverse
type: Item
instance of: scholarly article
title: Completing a symmetric \(2\times 2\) block matrix and its inverse
zbMATH Open document ID: 0848.15008
DOI: 10.1016/0024-3795(94)00144-8
author: Hua Dai
published in: Linear Algebra and its Applications
publication date: 1996-10-21T00:00:00Z
review text: The author considers the following completion problem: suppose we are given two nonegative integers \(n_1\), \(n_2\) such that \(n_1+ n_2= n>0\). Also suppose that we are given the matrices \(A_{11}\), \(A_{12}\), \(A_{21}\), and \(B_{22}\) having dimensions \(n_1 \times n\), \(n_1 \times n_2\), \(n_2 \times n_1\), and \(n_2 \times n_2\), respectively. Then the author determines necessary and sufficient conditions so that there exists an \(n_2 \times n_2\) matrix \(A_{22}\) such that \[ A= \left[ \begin{matrix} A_{11} &A_{12}\\ A_{21} &A_{22} \end{matrix} \right] \] and i) \(A\) is nonsingular and symmetric, and \(B_{22}\) is the lower right block of a partitioning of \(A^{-1}\), ii) \(A\) is symmetric positive definite, and \(B_{22}\) is the lower right block of a partitioning of \(A^{-1}\).
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 871123
zbMATH Keywords: symmetric block matrix
zbMATH Keywords: inverse
zbMATH Keywords: completion
reviewed by: Arbind Kumar Lal
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00144-8
OpenAlex ID: W2093567593
cites work: Maximal rank Hermitian completions of partially specified Hermitian matrices.
cites work: Q3831127
cites work: On the symmetric solutions of linear matrix equations
cites work: Completing a matrix when certain entries of its inverse are specified
cites work: Matrix Analysis
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description: scientific article; zbMATH DE number 871123