  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.
