Campus Units

Computer Science, Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

3-2006

Journal or Book Title

Linear Algebra and its Applications

Volume

413

DOI

10.1016/j.laa.2005.10.007

Abstract

A P-matrix is a real square matrix having every principal minor positive, and a Fischer matrix is a P-matrix that satisfies Fischer’s inequality for all principal submatrices. In this paper, all patterns of positions for n × n matrices, n ⩽ 4, are classified as to whether or not every partial Π-matrix can be completed to a Π-matrix for Π any of the classes positive P-, nonnegative P-, or Fischer matrices. Also, all symmetric patterns for 5 × 5 matrices are classified as to completion of partial Fischer matrices, and all but two such patterns are classified as to positive P- or nonnegative P-completion. We also show that any pattern whose digraph contains a minimally chordal symmetric-Hamiltonian induced subdigraph does not have Π-completion for Π any of the classes positive P-, nonnegative P-, Fischer matrices.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 413 (2006): 342, doi:10.1016/j.laa.2005.10.007. Posted with permission.

Rights

This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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