Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

5-2001

Journal or Book Title

Linear Algebra and its Applications

Volume

328

DOI

10.1016/S0024-3795(00)00299-8

Abstract

A pattern is a list of positions in an n×n real matrix. A matrix completion problem for the class of Π-matrices asks whether every partial Π-matrix whose specified entries are exactly the positions of the pattern can be completed to a Π-matrix. We survey the current state of research on Π-matrix completion problems for many subclasses Π of P0-matrices, including positive definite matrices, M-matrices, inverse M-matrices, P-matrices, and matrices defined by various sign symmetry and positivity conditions on P0- and P-matrices. Graph theoretic techniques used to study completion problems are discussed. Several new results are also presented, including the solution to the M0-matrix completion problem and the sign symmetric P0-matrix completion problem.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 328 (2001): 161, doi:10.1016/S0024-3795(00)00299-8. 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

Share

COinS