Year
2013
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
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
Abstract
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.
Suggested Citation
Chilstrom, Peter, "Singular Value Inequalities: New Approaches to Conjectures" (2013). UNF Graduate Theses and Dissertations. 443.
https://digitalcommons.unf.edu/etd/443