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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 $P$?

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