Nonsingularity criteria for matrices involving combinatorial considerations
type: Item
instance of: scholarly article
title: Nonsingularity criteria for matrices involving combinatorial considerations
zbMATH Open document ID: 0686.05036
DOI: 10.1016/0024-3795(88)90236-4
author: K. Appert
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: In this survey paper several related combinatorially-based singularity criteria for matrices over arbitrary fields are surveyed. The best way to express the focus of the paper is to list titles of the sections: 1. Introduction; elementary criteria for matrices over arbitrary fields; 2. L-matrices (sign nonsingularity); 3. Potential nonsingularity and complete matchings; 4. Stable nonsingularity; 5. Closed sets in graphs; 6. Another undirected graph of a matrix; acyclic matrices; 7. A nonsingularity criterion for irreducible acyclic matrices with zero diagonal; 8. A nonsingularity criterion for general combinatorially symmetric matrices. The results in last two paragraphs are taken from [\textit{D. Carlson} and \textit{D. Hershkowitz}, Nonsingularity criteria for general combinatorially symmetric matrices, Linear Algebra Appl. 114/115, 399-416 (1989; see the review above)].
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 4123772
zbMATH Keywords: nonsingularity
zbMATH Keywords: combintorial criteria
zbMATH Keywords: matrices over general fields
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90236-4
OpenAlex ID: W1978929267
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description: scientific article; zbMATH DE number 4123772