Date Approved

5-27-2016

Embargo Period

6-2-2016

Document Type

Thesis

Degree Name

M.A. Mathematics

Department

Mathematics

College

College of Science & Mathematics

Advisor

Nguyen, Hieu

Committee Member 1

Czochor, Ronald

Committee Member 2

Osler, Thomas

Keywords

Algorithms, Linear Algebra, Mathematics, Matrices, Partitions

Subject(s)

Frames (Vector analysis); Algorithms

Disciplines

Mathematics

Abstract

An open question stated by Marcus, Spielman, and Srivastava [10] asks "whether one can design an efficient algorithm to find the partitions guaranteed by Corollary 1.5." This corollary states that given a set of vectors in C whose outer products sum to the identity there exists a partition of these vectors such that norms of the outer-product sums of each subset satisfy an inequality bound. Here particular types of vector sets called finite frames are analyzed and constructed to satisfy the inequality described in Corollary 1.5. In this thesis, rigorous proofs and formulations of outer-product norms are utilized to find these partitions and to identify constraints on the finite frames in order to satisfy Corollary 1.5.

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