Date Thesis Awarded

5-2018

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Charles Johnson

Committee Members

Junping Shi

Mark Greer

Abstract

A matrix is called totally nonnegative (TN) if the determinant of

every square submatrix is nonnegative and totally positive (TP)

if the determinant of every square submatrix is positive. The TP

(TN) completion problem asks which partial matrices have a TP

(TN) completion. In this paper, several new TP-completable pat-

terns in 3-by-n matrices are identied. The relationship between

expansion and completability is developed based on the prior re-

sults about single unspecied entry. These results extend our un-

derstanding of TP-completable patterns. A new Ratio Theorem

related to TP-completability is introduced in this paper, and it can

possibly be a helpful tool in TP-completion problems.

Included in

Algebra Commons

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