Diagonalization of skew-Hermitian dual quaternion matrices and $\varphi$-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 $\varphi$, we also obtain the diagonalization result of $\varphi$-Hermitian dual quaternion matrices in the sense of unitary $\varphi$-congruence, which generalizes the Autonne--Takagi factorization of symmetric complex matrices and $\varphi$-Hermitian quaternion matrices.

arXiv comment13 pages