PreprintCC BY 4.0arXiv
Diagonalization of skew-Hermitian dual quaternion matrices and ϕ-Hermitian dual quaternion matrices
Abstract
In this article, we present the diagonalization of skew-Hermitian dual quaternion matrices in the sense of unitary equivalence. For a unit quaternion ϕ, we also obtain the diagonalization result of ϕ-Hermitian dual quaternion matrices in the sense of unitary ϕ-congruence, which generalizes the Autonne--Takagi factorization of symmetric complex matrices and ϕ-Hermitian quaternion matrices.
Related
- Unitary similarity for dual complex matrices and dual quaternion matrices
- Simultaneous diagonalization via congruence: Nondegenerate families of symmetric matrices
- Diagonalization of the Toda flow for arbitrary isospectral symmetric matrices
- Efficient Low-Rank Approximation of Quaternion Matrices via Adaptive Cross Approximation
- New Maximum Hermitian d-Codes and New Invariants from Skew Polynomial Rings
BibTeX
@misc{yao2026diagonalization,
title = {{Diagonalization of skew-Hermitian dual quaternion matrices and $ϕ$-Hermitian dual quaternion matrices}},
author = {Cailing Yao and Bingzhe Hou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14692},
eprint = {2610.14692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14692},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diagonalization of skew-Hermitian dual quaternion matrices and ϕ-Hermitian dual quaternion matrices
AU - Cailing Yao
AU - Bingzhe Hou
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14692
UR - https://arxiv.org/abs/2610.14692
AB - In this article, we present the diagonalization of skew-Hermitian dual quaternion matrices in the sense of unitary equivalence. For a unit quaternion ϕ, we also obtain the diagonalization result of ϕ-Hermitian dual quaternion matrices in the sense of unitary ϕ-congruence, which generalizes the Autonne--Takagi factorization of symmetric complex matrices and ϕ-Hermitian quaternion matrices.
ER -