Geodesic
On the Number of Positive Entries in the Powers of a Non-Negative Matrix
Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 525-537

Voir la notice de l'article provenant de la source Cambridge University Press

A real matrix A is said to be non-negative if and only if none of its entries is negative. Suppose A is an r by r non-negative matrix. We want to examine: (A) The first power of A to maximize the number of positive entries in An, (B) For each 1 ≤ i ≤ r the first power of A to maximize the number of positive entries in the i-th row of An. We shall call the former first power the index of A and the latter the i-th row index of A (index (i, A)). 
Pullman, N. On the Number of Positive Entries in the Powers of a Non-Negative Matrix. Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 525-537. doi: 10.4153/CMB-1964-049-x
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