I would like to convert the following condition for $x$ \begin{align} x = N \lambda, \lambda \geq 0 \end{align} to a pure linear inequality form, i.e. find an $L$ and eliminate $\lambda$ \begin{align} L x \leq 0 \end{align} The first condition basically means "$x$ is in the cone generated by the columns of $N$", hence the set $x$ lives in should be a polytope with all faces containing the origin, justifying the form $Lx \leq 0$. But how exactly can I express $L$ in terms of $N$?