Mathematics Faculty Articles

Title

Totally Positive Shapes and TPk-completable Patterns

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 TPk 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 TPk-completion problem and TPk-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

DOI

10.1016/j.laa.2011.05.027

Peer Reviewed

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