Moore Determinant of Dual Quaternion Hermitian Matrices

TL;DR

This paper extends the concept of determinants to dual quaternion Hermitian matrices, demonstrating their invariance properties and equivalence to eigenvalue products, thus advancing algebraic understanding of these matrices.

Contribution

It introduces the extension of Chen and Moore determinants to dual quaternion Hermitian matrices and proves their invariance and equality to eigenvalue products.

Findings

Chen determinant is invariant under matrix operations.

Chen and Moore determinants are equal for dual quaternion Hermitian matrices.

Determinants equal the product of eigenvalues.

Abstract

In this paper, we extend the Chen and Moore determinants of quaternion Hermitian} matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian {matrices is invariant under addition, switching, multiplication, and unitary operations at the both hand sides. We then show the Chen and Moore determinants of dual quaternion Hermitian matrices are equal to each other, and they are also equal to the products of eigenvalues. The characteristic polynomial of a dual quaternion Hermitian matrix is also studied.