Editing Perron–Frobenius theorem (section)

====Lemma====
Given a non-negative ''A'', assume there exists ''m'', such that ''A<sup>m</sup>'' is positive, then ''A''<sup>''m''+1</sup>, ''A''<sup>''m''+2</sup>, ''A''<sup>''m''+3</sup>,... are all positive.

''A''<sup>''m''+1</sup> = ''AA''<sup>''m''</sup>, so it can have zero element only if some row of ''A'' is entirely zero, but in this case the same row of ''A<sup>m</sup>'' will be zero.

Applying the same arguments as above for primitive matrices, prove the main claim.