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. (C) 2007 Elsevier Ltd. All rights reserved.
distribution and estimation eigenvalue real quaternion matrix generalized gerschgorin's theorem generalized rayleigh division