Thomas Cameron, Ph.D.

Assistant Professor, Mathematics
Office Phone
Office Location
18 Prischak
PENN STATE BEHREND
1 PRISCHAK BUILDING
ERIE PA 16563
Biography

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.

Research Interests

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

Publications

Mathematical Review of set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting - August 28, 2020

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

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

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

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

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

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

Education

Ph D, Mathematics, Washington State University

MS, Mathematics, Washington State University

BS, Mathematics, University of Minnesota Duluth

AA, General Liberal Arts, Century College