Numerical ranges and matrix completions
type: Item
instance of: scholarly article
title: Numerical ranges and matrix completions
zbMATH Open document ID: 0960.15023
DOI: 10.1016/S0024-3795(00)00135-X
author: R. Smith
published in: Linear Algebra and its Applications
publication date: 2001-05-01T00:00:00Z
review text: For a partial matrix \(T\) on a pattern \(\mathcal P\) let \(W_1(T)\) be its inner numerical range and \(W_2(T)\) be its outer numerical range. The authors show that \(W_1(T)=W_2(T)\) for every partial matrix \(T\) on \(\mathcal P\) if and only if a graph associated with the pattern is chordal. This extends one result of \textit{C. R. Johnson} and \textit{M. E. Lundquist} [Operator Theory: Adv. Appl. 50, 283-291 (1991; Zbl 0735.15021)] to patterns which are not necessarily reflexive and symmetric.
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 1523267
zbMATH Keywords: matrix completion
zbMATH Keywords: inner numerical range
zbMATH Keywords: chordal graph
zbMATH Keywords: outer numerical range
zbMATH Keywords: partial matrix
reviewed by: A. R. Alimov
MaRDI profile type: Publication
cites work: Positive definite completions of partial Hermitian matrices
cites work: Q5521075
cites work: Q4040931
cites work: Q3973568
Wikidata QID: Q127391144
description: scientific article; zbMATH DE number 1523267