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.