Distortions of Toeplitz Matrices
Mentor:Tyler McMillen, Professor of Math, California State University, Fullerton
I will present results on the effects of distorting Toeplitz matrices by allowing their diagonals to vary slowly. Toeplitz matrices are important in Gaussian distributions and error predictions within mathematics but are also used in other fields including image restoration, noise cancellation, and speech enhancement. Although Toeplitz matrices are important in many applications, most of the matrices that arise in applications are not Toeplitz. My project is to explore how the known results for Toeplitz matrices extend to distorted Toeplitz matrices. Our approach to this problem is to look at the spectrum of a Toeplitz matrix and observe how it changes after distorting the matrix. I will present visual results on a few of these Toeplitz matrices and their distortions.