2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153932Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function. A matrix analogue of Maréchal's extended perspectives provides additional inequalities, including a $p+q\leq 1$ result of Lieb.Mathematical PhysicsInformation Theory81P68text