Mathematics Faculty Articles

Title

Complete Solution to the TP2 Completion Problem

Document Type

Article

Publication Date

2014

Publication Title

Linear and Multilinear Algebra

Keywords

Bruhat order, Finite generated cone, Matrix completion problem, Partial orders on nonnegative matrices, Totally positive matrix, TP2 matrix

ISSN

0308-1087

Volume

62

Issue/No.

10

First Page

1403

Last Page

1420

Abstract

For any pattern of the specified entries, an explicit finite list of polynomial inequalities in the specified entries is given that characterizes the completability of a partial positive matrix to a TP2 matrix. Each polynomial happens to be a monomial, and an algorithm, whose input is the pattern, is given for finding the polynomials. The method uses some new partial orders on matrices and the logarithmic method to reduce the question to determining the generators of a certain finitely generated, pointed cone.

Comments

AMS Subject Classifications: 15A83, 15B48, 06A06

DOI

10.1080/03081087.2013.831093

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