Schur complements and its applications to symmetric nonnegative and \(Z\)-matrices
type: Item
instance of: scholarly article
title: Schur complements and its applications to symmetric nonnegative and \(Z\)-matrices
zbMATH Open document ID: 1006.15020
DOI: 10.1016/S0024-3795(02)00327-0
published in: Linear Algebra and its Applications
publication date: 2002-09-12T00:00:00Z
review text: The Schur complement \(H/A\) of a nonsingular principal submatrix \(A\) of a matrix \(H\) is a useful tool in matrix analysis. When \(H\) is irreducible nonnegative, the Perron complement is another interesting concept. For a Hermitian semidifinite matrix \(H\), the author obtains interlacing results for the eigenvalues of \(H\) and those of \(H/A\), refining the ones obtained by \textit{R. L. Smith} [Linear Algebra Appl. 177, 137-144 (1992; Zbl 0765.15007)]. For irreducible nonnegative matrices, analogous results involving Perron complements are also obtained. Perron complements are also used to get some bounds for the eigenvalues of irreducible symmetric nonnegative matrices and for irreducible symmetric \(Z\)-matrices, that are real matrices whose off-diagonal entries are nonpositive.
reviewed by: M. Gasca
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1800365
zbMATH Keywords: Schur complement
zbMATH Keywords: Perron complement
zbMATH Keywords: eigenvalues interlacing
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: \(Z\)-matrices
author: Yizheng Fan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1800365