%0 Journal Article %T Notes on Greub-Rheinboldt inequalities %A Di Zhao %A Hongyi Li and Zhiguo Gong %J Journal of Inequalities and Applications %D 2013 %I %R 10.1186/1029-242X-2013-7 %X In this paper, we focus on matrix Greub-Rheinboldt inequalities for commutative positive definite Hermitian matrix pairs. Some improvements, which yield sharpened bounds compared with existing results, are presented. %U http://www.journalofinequalitiesandapplications.com/content/2013/1/7/abstract