Year of Publication


Season of Publication


Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

First Advisor

Dr. Raluca Dumitru

Second Advisor

Dr. Scott Hochwald

Third Advisor

Dr. Mei-Qin Zhan

Department Chair

Dr. Scott Hochwald

College Dean

Dr. Barbara A. Hetrick


Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.