Research and Projects

Interests

I am interested in topics in linear algebra and my current work deals specifically with the GMRES algorithm (a Krylov projection method for solving linear systems).

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.