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
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