The inertia of Hermitian block matrices with zero main diagonal
type: Item
instance of: scholarly article
title: The inertia of Hermitian block matrices with zero main diagonal
zbMATH Open document ID: 0961.15013
DOI: 10.1016/S0024-3795(00)00089-6
published in: Linear Algebra and its Applications
publication date: 2001-05-28T00:00:00Z
review text: The inertia of a Hermitian block matrix \(H\) is characterized when \(H\) has a \(3\times 3\) block decomposition with null blocks on the main diagonal. Given nonnegative integers \(n_i\), \(i=1,2,3\) and the numbers \(r_{ij}\), \(R_{ij}\), \(i<j\leq 3\) such that \(0\leq r_{ij}\leq R_{ij} \leq\min \{n_i,n_j\}\), equivalent conditions with the following statement (i) are emphasized: (i) There exist \(n_i\times n_j\) matrices \(X_{ij}\), \(i<j\leq 3\) such that \(r_{ij}\leq\text{rank} X_{ij}\leq R_{ij}\) and \[ H=\left [\begin{matrix} 0 & X_{12} & X_{13} \\ X^*_{12} & 0 & X_{23}\\ X^*_{13} & X^*_{23} & 0\end{matrix} \right] \] has inertia \((\pi,\nu,*)\).
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1462181
zbMATH Keywords: rank
zbMATH Keywords: inequalities
zbMATH Keywords: inertia
zbMATH Keywords: Hermitian block matrix
author: C. M.da Fonseca
MaRDI profile type: Publication
cites work: The inertia of hermitian matrices with a prescribed 2×2 block decomposition
cites work: The inertia of certain Hermitian skew-triangular block matrices
cites work: On the interia of some classes of partitioned matrices
cites work: Q5811214
description: scientific article; zbMATH DE number 1462181