How to determine the convexity of the following functions:
$X^p$, in which $p$ is a real number and $X$ is $n \times n$ symmetric positive definite matrix.
$e^X$ in which $X$ is a $n \times n$ symmetric matrix and $n \geq 2$
The convexity mentioned above refers to the proper cone $S^n_{+}$.
Thanks a lot!