Jacobi method for dual quaternion Hermitian eigenvalue problems and applications

Abstract

Eigenvalue decomposition of quaternion Hermitian matrices is a crucial mathematical tool for color image reconstruction and recognition. Quaternion Jacobi method is one of the classical methods to compute the eigenvalues of a quaternion Hermitian matrix. Using quaternion Jacobi rotations, this paper brings forward an innovative method for the eigenvalue decomposition of dual quaternion Hermitian matrices. The effectiveness of the proposed method is confirmed through numerical experiments. Furthermore, a dual complex matrix representation for the color image is developed, and the dual quaternion Jacobi method is applied to the eigenvalue problems of dual complex Hermitian matrices. This approach achieves successful results in the color images reconstruction and recognition. Compared to the quaternion matrix representation of the color image, this approach makes computations more convenient when dealing with problems related to color image processing.