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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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This is not a real question. What do you want to know? –  Mariano Suárez-Alvarez Dec 2 '11 at 7:28
    
I want to know the definition of primitive matrices? –  Zizo Dec 2 '11 at 7:30
    
I've reformatted the question what do you think of it now? –  Zizo Dec 2 '11 at 7:32
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Wikipedia uses the definition you gave. –  lhf Dec 2 '11 at 11:04

1 Answer 1

up vote 1 down vote accepted

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. –  Zizo Dec 4 '11 at 6:17

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