Suppose that $A \in \mathbb{R}^{n \times n}$ and $B \in \mathbb{R}^{n \times m}$ are integer matrices. Let $P$ be the unbounded polytope in $\mathbb{R}^n$ given by $$B \cdot x \geq 0$$
As there is no explicit formula for the roots of high degree polynomials we cannot explictily compute the eigenvalues or eigenvectors of $A$ however:
Is there an algorithm to determine if there is an eigenvector of $A$ lying inside of $P$?