A Mirsky-Type Unitarily Invariant Norm Inequality for Dual Quaternion Matrices and Its Applications

In this paper, we present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices. By using this unitarily invariant norm inequality, we obtain some other unitarily invariant norm inequalities for dual quaternion matrices, including the low-rank approximation problem, eigenvalue perturbation theorem and polar decomposition. Some inequalities for the difference between singular values and eigenvalues of two dual quaternion matrices under the Frobenius norm are extended.