Let $f: \Bbb R^n \rightarrow \Bbb R$ be a convex function.
Define $\text{epi}(f)=\{(x,t) | f(x) \le t\}$.
If $w \ge 0$ then $\text{epi}(wf) = \left[ \begin{array}{cc} I&0\\ 0&w \end{array} \right] \text{epi}(f)$ is convex.
What does the notation $\left[ \begin{array}{cc} I&0\\ 0&w \end{array} \right] \text{epi}(f)$ mean? It looks like the product of a matrix and a set. Can someone explain what this notation means and why these two things are equal?
Apply mat multiply to each point of the set: $M(x,t)^T$.