A survey with new examples and a new Popoviciu-type inequality for strongly superadditive functions, derived from weak majorization.
Completely strong superadditivity of generalized matrix functions
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abstract
We prove that generalized matrix functions satisfy a block-matrix strong superadditivity inequality over the cone of positive semidefinite matrices. Our result extends a recent result of Paksoy-Turkmen-Zhang (V. Paksoy, R. Turkmen, F. Zhang, Inequalities of generalized matrix functions via tensor products, Electron. J. Linear Algebra 27 (2014) 332-341.). As an application, we obtain a short proof of a classical inequality of Thompson (1961) on block matrix determinants.
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Old and New on Strongly Subadditive/Superadditive Functions
A survey with new examples and a new Popoviciu-type inequality for strongly superadditive functions, derived from weak majorization.