Date of Publication

8-2025

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Honor/Award

Outstanding Thesis Award Nominee

Thesis Advisor

Daryl Q. Granario

Defense Panel Chair

Francis Joseph H. Campena

Defense Panel Member

Rafael Reno S. Cantuba

Abstract/Summary

A nonsingular n × n matrix A is said to be initially positive (IP) if the first column of A and the first row of A^{-1} are both positive. IP matrices are used to construct matrices with negative entries that still satisfy the Perron-Frobenius property. In this paper, we provide ways to construct IP matrices for any order n by conic condition, geometric-combinatorial duality of convex polyhedra, and linear algebraic duality. We provide geometric characterizations of IP matrices via cones and simplices. We also present an elementary characterization of IP matrices via cofactors and determinant. We then provide a characterization of IP via combinatorial matrix theory by providing a list of sign patterns that require or allow IP for small orders.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Matrices; Combinatorial analysis

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Embargo Period

8-11-2027

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Available for download on Wednesday, August 11, 2027

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