Date of Award
2025
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
Kottke, Christopher
Area of Concentration
Mathematics
Abstract
In this thesis, we study several Riemannian metrics equipped to the manifold of Symmetric Positive-Definite (SPD) matrices. Emphasizing the “Scaling-Rotation Curves” of [10], we generalize this approach to pairs of nonsquare matrices of equal rank. Using computer software, we search for a heuristic to mitigate the poor performance of this geodesic as matrix size increases, but no pattern reveals itself. We conclude by suggesting investigation of other possible generalizations for nonlinear interpolation of nonsquare matrices.
Recommended Citation
Stuart, Braedan, "SCALING-ROTATION CURVES ON MATRICES OF CONSTANT
RANK" (2025). Theses & ETDs. 6643.
https://digitalcommons.ncf.edu/theses_etds/6643