On the Number of Positive Entries in the Powers of a Non-Negative Matrix
Norman J. Pullman · Canadian Mathematical Bulletin · 1964
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 A n , (B) For each 1 ≤ i ≤ r the first power of A to maximize the number of positive entries in the i-th row of A n . We shall call the former first power the index of A and the latter the i-th row index of A (index (i, A)).