grandes-ecoles 2025 Q14

grandes-ecoles · France · x-ens-maths-d__mp Matrices Linear Transformation and Endomorphism Properties

Let $n \geq 1$ be an integer and $P \subset \mathbb{R}^n$ a polytope. Let $V$ be the set of vertices of $P$. Show that $P = \operatorname{Conv}(V)$.

Let $n \geq 1$ be an integer and $P \subset \mathbb{R}^n$ a polytope. Let $V$ be the set of vertices of $P$. Show that $P = \operatorname{Conv}(V)$.