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Is this definition for primitive matrices correct?

A square matrix $P \geqslant 0$ is called primitive if there exists a power $k$ such that $P^k > 0,$ that is, there exists a $k$ such that for all ${ij},$ the entries $ij$ are positive.

I read it in the Internet but it was not referenced.

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    [Wikipedia](http://en.wikipedia.org/wiki/Perron–Frobenius_theorem#Classification_of_matrices) uses the definition you ga$v$e.2011-12-02

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Horn and Johnson agrees. Could also define as nonnegative matrix that is irreducible and has just one eigenvalue of maximum modulus.

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    Thanks. This really helped me.2011-12-04