Quaternion Toeplitz matrices and their fundamental properties

2025/10/05 by Khan, Muhammad Ahsan, Khan, Sohail
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.04297

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 quaternions 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.

Citations

• Block Toeplitz Matrices: Multiplicative Properties
• On, Around, and Beyond Frobenius' Theorem on Division Algebras
• Algebras of block Toeplitz matrices with commuting entries
• Every matrix is a product of Toeplitz matrices
• Lectures on Linear Algebra over Division Ring
• Quaternions and matrices of quaternions

Related

• Hermitian Quaternion Toeplitz Matrices by Quaternion-valued Generating Functions
• Matrix Theory over the Complex Quaternion Algebra
• A Simple Proof of the Classification of Normal Toeplitz Matrices
• Weyl distributions, spectral properties, and circulant approximation results for quaternion block multilevel Toeplitz matrix sequences
• Quaternionic quasideterminants and determinants