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

Abstract: 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. [Copyright &y& Elsevier]