The estimation of eigenvalues of sum, difference, and tensor product of matrices over quaternion division algebra

In this paper, the estimation problems of eigenvalues of sum, difference, and tensor product of matrices over quaternion division algebra are studied. A pair of inequalities about eigenvalues of self-conjugate quaternion matrix is established, the famous Brauer Theorem is generalized to quaternion division algebra and the form of Cassini Theorem over quaternion division algebra is also worked out successfully.