Primitive nonnegative matrix
= Primitive nonnegative matrix
A square <nonnegative matrix> $A$ is primitive if some positive integer power $A^k$ has strictly positive entries. It is therefore an <irreducible nonnegative matrix>. The <Perron–Frobenius theorem> gives a leading <eigenvalue> whose <modulus> is strictly larger than that of every other <eigenvalue>. Every strictly positive <matrix> is primitive; the two-cycle permutation <matrix> is irreducible but not primitive.