Quaternion Toeplitz matrices and their fundamental properties

Abstract

Toeplitz matrices are characterized by their constant diagonals, have been extensively studied in various settings, including over real and complex numbers. However, their study over quaternion is quite sparse. In this paper, we investigate the structure and the algebraic properties of quaternion Toeplitz matrices. Most importantly, we established a complete characterization of all normal  Toeplitz matrices having entries commutative quaternions.