On completion problems for various classes of P-matrices

Thumbnail Image
Date
2006-03-01
Authors
Bowers, John
Evers, Job
Hogben, Leslie
Shaner, Steve
Snider, Karyn
Wangsness, Amy
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
Organizational Unit
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Computer ScienceMathematics
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.

Description
Keywords
Citation
DOI
Copyright
Sat Jan 01 00:00:00 UTC 2005
Collections