Year: 2026
Type: preprint
Abstract: Let $ϕ$ be a quaternion of modulus $1$. In this article, we study some topics related to $ϕ$-conjugation for quaternionic matrices, including $ϕ$-Hermitian matrices, $ϕ$-conjugate normal matrices, unitary $ϕ$-congruence and $ϕ$-HSH decomposition (decomposition of a $ϕ$-Hermitian matrix and a skew $ϕ$-Hermitian matrix). In particular, we generalize the Autonne-Takagi factorization of quaternion $ϕ$-Hermitian matrices for all unit quaternion $ϕ$. This gives an affirmative answer to a problem proposed by R. Horn and F. Zhang in the paper ``A generalization of the complex Autonne-Takagi factorization to quaternion matrices, Linear Multilinear A. 60: 1239--1244, 2012''.
Source: arXiv (Cornell University)
Authors: Yao, Cailing, Hou, Bingzhe, Xin, Yue
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213997202