Journal of Inequalities and Applications
Volume 2005 (2005), Issue 5, Pages 449-458

Some inequalities for sums of nonnegative definite matrices in quaternions

Yongge Tian1 and George P. H. Styan2

1School of Economics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, China
2Department of Mathematics and Statistics, McGill University, Montréal, Québec H3A 2K6, Canada

Received 9 January 2004; Revised 24 December 2004

Copyright © 2005 Yongge Tian and George P. H. Styan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some matrix versions of the Cauchy-Schwarz and Frucht-Kantorovich inequalities are established over the quaternionic algebra. As applications, a group of inequalities for sums of Hermitian nonnegative definite matrices over the quaternionic algebra are derived.