Totally Positive Shapes and TP_k-completable Patterns

Authors

D. Hoff, University of Minnesota
C. R. Johnson, College of William and Mary
Shahla Nasserasr, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

6-15-2012

Publication Title

Linear Algebra and its Applications

Keywords

Matrix completion problem, Totally positive matrix, TPk matrix

ISSN

0024-3795

Volume

436

Issue/No.

12

First Page

4412

Last Page

4422

Abstract

The notions of total positivity and of TP_k are generalized to “shapes” (a generalization of matrices). In particular, the relationship between positivity of “contiguous” minors and all minors is characterized for general shapes and for certain special types of shapes. This and other ideas are used to address the TP_k-completion problem and TP_k-completable patterns. In case k=2, a near characterization of TP₂-completable patterns is given.

Comments

Under an Elsevier user license

AMS classification

• 15A83;
• 15B48

NSUWorks Citation

Hoff, D.; Johnson, C. R.; and Nasserasr, Shahla, "Totally Positive Shapes and TP_k-completable Patterns" (2012). Mathematics Faculty Articles. 127.
https://nsuworks.nova.edu/math_facarticles/127

DOI

10.1016/j.laa.2011.05.027