Let $P = \{ x \in \mathbb{R}^n \mid Ax \leq b \}$ be a (bounded) polyhedron for $A \in \mathbb{R}^{m \times n}$ and $b \in \mathbb{R}^m$, $n,m > 0$.


Moreover, let $M \colon \mathbb{R}^n \to \mathbb{R}^p$ be a linear map for $p \leq n$.


I'm interested in computing a $\mathcal{H}$-representation of $M \cdot P = \{Cx \mid x \in P\}.$ Are there any known algorithms, besides the "Quantifier elimination for linear arithmetic" as pointed out in [1](https://math.stackexchange.com/questions/184955/how-to-compute-the-image-of-a-polyhedron-under-a-linear-transformation)?



$\mathcal{H}$-polyhedron under a linear map
Yes, by the [Motzkin Double Description Method](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.8343) you compute the $V$-representation of $P,$ hence the $V$-representation of $M P,$ then, by the double description method (again) the $H$-representation of $M P.$


