The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems in this field. These include convexity principles which play an essential role in the Lieb-Ruskai proof of the strong subadditivity of quantum entropy.

翻译：结合预解式演算，经典的凸性二阶导数检验被证明是研究凸矩阵值函数的有力工具。我们通过该领域的一系列定理展示了这一方法的适用性。其中包括在Lieb-Ruskai证明量子熵强次可加性过程中起核心作用的凸性原理。