Let \(\mat{F},\mat{G}\) be positive definite matrices (do they have to be definite?) and \(0 \leq p \leq 2.\) Show that \[ \tr\left(\mat{F}^{p/2} - \mat{G}^{p/2}\right) \leq \frac{p}{2} \tr\left((\mat{F} - \mat{G})\mat{G}^{p/2 - 1}\right). \] I’m working on it. See if you can get a proof before I do