Distribution and estimation for eigenvalues of real quaternion matrices

In this paper, the concept of generalized spherical neighborhood on the real quaternion field is introduced. Then, Schwartz’ s inequality and the Gerschgorin’s theorem are proved on the real quaternion field and the problems of the distribution and estimation of real quaternion matrix eigenvalues are solved. Finally, some upper bound and lower bound estimation theorems for the moment, the real and imaginary part of the real quaternion matrices eigenvalues are obtained.