Date of Publication

2023

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Daryl Q. Granario

Defense Panel Chair

Rafael Reno S. Cantuba

Defense Panel Member

John Vincent S. Morales
Paul Reine Kennett L. Dela Rosa

Abstract/Summary

Let A∈GL(n,ℂ). Let S1={β1,β2,...,βn} and S2={γ1,γ2,...,γn} be subsets of ℂ\{0}. We say that A realizes (S1,S2) if there exist B,C∈GL(n,ℂ) such that A=BC with σ(B)=S1 and σ(C)=S2. If both B,C are from a subgroup G≤GL(n,ℂ), we say that (S1,S2) is realized by A in G. Sourour showed that if S1={β1,β2,...,βn} and S2={γ1,γ2,...,γn}⊆𝔽\{0} are given, a nonscalar A∈GL(n,𝔽) realizes (S1,S2) if and only if det A=Π_(j=1)^n βjγj. We take G to be the 2nx2n symplectic group Sp(2n,ℂ) and determine if there exists pair of sets (S1,S2) which are realizable by a matrix A∈Sp(4,ℂ).

Abstract Format

html

Language

English

Format

Electronic

Physical Description

[45 leaves]

Keywords

Factorization (Mathematics); Matrices

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Embargo Period

8-11-2023

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