Completely strong superadditivity of generalized matrix functions

Minghua Lin; Suvrit Sra

Completely strong superadditivity of generalized matrix functions

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arxiv 1410.1958 v1 pith:Q2GDPAIA submitted 2014-10-08 math.FA

Minghua Lin , Suvrit Sra This is my paper · ORCID

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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
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A survey with new examples and a new Popoviciu-type inequality for strongly superadditive functions, derived from weak majorization.

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