Date Thesis Awarded

12-2019

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Charles Johnson

Committee Members

Timothy Davis

Christopher Vinroot

Abstract

A n-by-n matrix A is said to be eventually positive if there is a power k such that $A^k$ is entrywise positive, and all subsequent powers are also entrywise positive. Here we provide an expression for the smallest such exponent of a 2-by-2 eventually positive matrix in terms of its entries; we also show that if the graph of an eventually positive matrix is a tree, then the positive part of that matrix must be primitive.

Included in

Algebra Commons

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