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A generalized reverse Cauchy inequality for matrices

Authors: 

Dinh Trung Hoa, Vo Thi Bich Khue & Hiroyuki Osaka

Source title: 
Linear and Multilinear Algebra, 64(7): 1415-1423, 2015 (ISI)
Academic year of acceptance: 
2015-2016
Abstract: 

We consider the generalized reverse Cauchy inequality for two positive definite matrices A and B and show that the generalized reverse Cauchy inequalities hold under the condition that AB + BA is positive. We note that this condition is critical for this inequality. Moreover, we show that the generalized reverse Cauchy inequality and the generalized Powers–Størmer inequality hold with respect to the unitarily invariant norms under the same condition.