Year
2025
Season
Spring
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
Committee Chairperson
Dr. Jose Franco
Second Advisor
Dr. Malgorzata Czerwinska
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Raluca Dumitru
Fourth Advisor
Dr. Allan Merino
Department Chair
Dr. Richard Patterson
College Dean
Dr. Kaveri Subrahmanyam
Abstract
In this thesis, we study matrix means from a geometric point of view. In particular, we consider divergences of the form Tr[A + B − 2G(A, B)] for certain Geometric-Type matrix means G(A, B). We derive alternative formulations of this distance function through the application of one-sided inverses of G(A, B). When G(A, B) = A#B, we give a curve parametrization of the straight-line path between two points with respect to this semi-metric and present conditions under which this holds for other Geometric-Type means. For read- ability and self-containment, we introduce most of the preliminary concepts to build up to our main goals.
Suggested Citation
DuBois, Blaine, "Geometric properties of positive definite matrices: Means, order, and metrics" (2025). UNF Graduate Theses and Dissertations. 1345.
https://digitalcommons.unf.edu/etd/1345