The inertia of certain Hermitian block matrices
type: Item
instance of: scholarly article
title: The inertia of certain Hermitian block matrices
zbMATH Open document ID: 0929.15019
DOI: 10.1016/S0024-3795(97)00338-8
published in: Linear Algebra and its Applications
publication date: 1999-05-05T00:00:00Z
review text: Hermitian matrices partitioned as \[ H=\left [\begin{matrix} H_1 & X_{12} & X_{13}\\ X^*_{12} & H_2 & 0\\ X^*_{13} & 0 & H_3 \end{matrix} \right] \] are considered. Sets of inertias of such matrices are characterized by a system of inequalities involving the orders of the blocks, the inertias of the blocks \(H_i\) and the ranks of the blocks \(X_{1j}\), \(j=2,3\). The main result generalizes a theorem of \textit{B. E. Cain} and \textit{E. Marques de Sá} [ibid. 160, 75-87 (1992; Zbl 0752.15002)] concerning partitioned matrices with null block \(H_3\). This main result is generalized to \(p\times p\) block decomposition of Hermitian matrices, \(p\geq 3\).
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1154661
zbMATH Keywords: Hermitian block matrix
zbMATH Keywords: inertia
zbMATH Keywords: system of inequalities
author: C. M.da Fonseca
MaRDI profile type: Publication
cites work: The inertia of a Hermitian matrix having prescribed complementary principal submatrices
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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
cites work: On the inertia of sums of Hermitian matrices
Wikidata QID: Q126644263
description: scientific article; zbMATH DE number 1154661