On completion problems for various classes of \(P\)-matrices
type: Item
instance of: scholarly article
title: On completion problems for various classes of \(P\)-matrices
zbMATH Open document ID: 1095.15016
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 2006-03-22T00:00:00Z
review text: A \(P\)-matrix is a real square matrix having every principal minor positive; a Fischer matrix is a \(P\)-matrix satisfying Fischer's inequality for all principal submatrices, i.e., \(\det A[\alpha] \det A[\beta] \geq \det A[\alpha \cup \beta]\) where \(\alpha, \beta \in 2^{\{1, ..., n\}}\) with \(\alpha \cap \beta = \emptyset\). The authors classify all patterns of positions for \((n \times n)\)-matrices, \(n \leq 4\), as to whether or not every partial positive \(P\)-matrix (non-negative \(P\)-matrix, Fischer matrix, respectively) can be completed to a matrix of the respective class.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 5014288
zbMATH Keywords: matrix completion
zbMATH Keywords: Fischer matrix
zbMATH Keywords: partial matrix
zbMATH Keywords: nonnegative \(P\)-matrix
zbMATH Keywords: weakly sign-symmetric \(P\)-matrix
zbMATH Keywords: determinant
zbMATH Keywords: inequalities involving determinants
MaRDI profile type: Publication
full work available at URL: j.laa.2005.10.007
OpenAlex ID: W2026025392
cites work: The nonnegative P_0-matrix completion problem
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cites work: Completions of P-matrix patterns
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cites work: Completions of partial \(P\)-matrices with acyclic or non-acyclic associated graph
cites work: A connection between positive semidefinite and Euclidean distance matrix completion problems
DOI: 10.1016/J.LAA.2005.10.007
description: scientific article; zbMATH DE number 5014288