Senior Thesis: Norms on Complex Matrices Induced by Random Vectors

For my senior thesis in math at Pomona, I completed a 60-page thesis containing original proofs of the main theorems, co-wrote and published two papers with my professors, and presented my work.

Both papers were published in the Canadian Mathematical Bulletin.

Published Work

“Norms on Complex Matrices Induced by Random Vectors.” This paper, published before I completed my thesis work, defines a class of random vector norms. I contributed the bit about the Pareto distribution and not much else.

Published in the Canadian Mathematical Bulletin, 2022. Cambridge · arXiv

The second paper, “Norms on Complex Matrices Induced by Random Vectors II: Extension of Weakly Unitarily Invariant Norms,” is substantially based on my thesis, including my novel proofs. It clarifies the definition of random vector norms and extends them beyond Hermitian matrices.

Published in the Canadian Mathematical Bulletin, 2023. Cambridge · arXiv

Thesis

Read the full thesis (PDF) — 60 pages of original proofs on norms induced by random vectors.