Research and Projects

Interests

My research focuses on numerical linear algebra (NLA), specifically in the intersection of QR algorithms, symmetric eigenvalue problems, and SVD algorithms. I have some experience in iterative algorithms for nonsymmetric linear systems, such as GMRES and various deflation strategies. In the future, I hope to dip more into randomized NLA algorithms that are in the spotlight right now.

Project: Vampire Matrices

Recently I have been exploring a special type of matrices sometimes called vampire matrices, which became popular from Matt Parker’s YouTube video in 2020. The original vampire matrix is a square matrix $A$, usually $2 \times 2$ or $3\times 3$, with integer entries between $1$ and $9$ such that $A^2=11A$. I have worked on generalizing such matrices to include $d$ digit numbers and to include more terms in the matrix equation. A brief overview is given in a recent conference presentation in March 2024. Anyone that is looking to collaborate on this project should reach out!