Thomas Cameron, Ph.D.

Assistant Professor, Mathematics
87 Benson
Mailing Address:
PENN STATE BEHREND
1 PRISCHAK BUILDING
ERIE PA 16563

Thomas R. Cameron is an assistant professor of Mathematics at Penn State Behrend. He is a passionate mathematics teacher and scholar whose interests lie at the intersection of algebraic graph theory, data science, and numerical analysis. In particular, his work has made notable contributions to the area of matrix polynomials, the numerical solution of polynomial equations, the characterization of digraphs, and the rankability of data.

Numerical linear algebra: study of matrix polynomials, the non-linear eigenvalue problem, and the numerical solution of polynomial roots; Algebraic graph theory: study of graphs using the algebraic properties of their associated matrices; Rankability of data: study of data and its inherent characteristics that make it more or less suitable for ranking

On the Laplacian spread of digraphs, Linear Algebra and its Applications - May, 2023
Collaborators: Wayne Barrett; Emily Evans; H. Tracy Hall; Mark Kempton

Constructions of cospectral graphs with different zero forcing parameters, Electronic Journal of Linear Algebra - May 5, 2022
Collaborators: Aid Abiad; Boris Brimkov; Jane Breen; Himanshu Gupta; Ralihe Villagran

On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots, Electronic Transactions of Numerical Analysis - March 21, 2022
Collaborator: Stef Graillat

On digraphs with polygonal restricted numerical range, Linear Algebra and its Applications - March 1, 2022
Collaborators: Tracy Hall; Ben Small; Alex Wiedemann

Mathematical Review of mth roots of H-selfadjoint matrices - September 1, 2021

On the Linear Ordering Problem and the Rankability of Data, Foundations of Data Science - June, 2021
Collaborators: Sebastian Charmot; Jonad Pulaj, Co-Author

Mathematical Review of set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting - November 6, 2020

On the restricted numerical range of the Laplacian matrix for digraphs, Linear and Multilinear Algebra - April 9, 2020
Collaborators: Michael Robertson; A. Wiedemann, Co-Author

On the graph Laplacian and the rankability of data, Linear Algebra and its Applications - March 1, 2020
Collaborators: A. N. Langville, Co-Author; H. C. Smith, Co-Author

On Householder sets for matrix polynomials, Linear Algebra and its Applications - January 15, 2020
Collaborator: P. J. Psarrakos, Co-Author

An effective implementation of a modified Laguerre method for the roots of a polynomial, Numerical Algorithms - 2019

On Descartes’ rule of signs for matrix polynomials, Operators and Matrices - 2019
Collaborator: P. J. Psarrakos, Co-Author

Finite precision in an infinite world, Math Horizons - August 30, 2019
Collaborator: T. P. Chartier, Co-Author

The determinant from signed volume to the Laplace expansion, American Mathematical Monthly - May 10, 2019

On the reduction of matrix polynomials to Hessenberg form, Electronic Journal of Linear Algebra - February 5, 2016

Spectral bounds for matrix polynomials with unitary coefficients, Electronic Journal of Linear Algebra - February 8, 2015

Ph D, Mathematics, Washington State University

MS, Mathematics, Washington State University

BS, Mathematics, University of Minnesota Duluth

AA, General Liberal Arts, Century College