Mathematics Faculty Articles

Title

TP_k Completion of Patterns with One Unspecified Entry

Document Type

Article

Publication Date

6-1-2014

Publication Title

Electronic Journal of Linear Algebra

Keywords

Totally positive-k matrix, Completion problem, Pattern, Polynomial conditions

ISSN

1081-3810

Volume

27

First Page

426

Last Page

443

Abstract

Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) completion. For a given m-by-n pattern with one unspecified entry, the minimum set of conditions characterizing TP3 completability is given. These conditions are at most eight polynomial inequalities on the specified entries of the pattern. For k ≥ 3, patterns with one unspecified entry that are TPk completable are also characterized, and conditions are described for completability otherwise

Comments

AMS subject classifications. 15A83, 15B48

DOI

10.13001/1081-3810.1628