Quaternion Toeplitz matrices and their fundamental properties

Muhammad Ahsan Khan; Shabana I. Khan

doi:10.48550/arxiv.2510.04297

October 5, 2025Open Access

Quaternion Toeplitz matrices and their fundamental properties

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Key Points

Quaternion toeplitz matrices exhibit constant diagonals, expanding the understanding of matrix structures.
We established a full characterization of normal matrices with commutative quaternion entries, enhancing algebraic analysis.
The study fills a gap in literature regarding algebraic properties of eigenvalues and eigenvectors in quaternion contexts.
These findings may pave the way for new developments in applied mathematics fields leveraging quaternion analysis.

Implication

This research reveals a complete characterization of normal toeplitz matrices over quaternions, suggesting new algebraic insights.

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.

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Cite This Study

Khan et al. (2025) studied this question.

synapsesocial.com/papers/68e962596210319498c300ba https://doi.org/10.48550/arxiv.2510.04297

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Quaternion Toeplitz matrices and their fundamental properties

Key Points

Implication

Abstract

Discussion

Cite This Study

Quaternion Toeplitz matrices and their fundamental properties

Key Points

Implication

Abstract

Discussion

Cite This Study

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