Julian D'Costa

Eventual Nonnegativity of a Matrix Is in P

Given a rational matrix $A$, is every sufficiently large power $A^n$ entrywise nonnegative? We prove that this problem is decidable in deterministic polynomial time. This is in contrast with deciding eventual nonnegativity of a single prescribed entry sequence $(A^n)_{ij}$, which amounts to the Ultimate Positivity Prob...