Weight properties of primitive matrices

For non- negative n x n matrices (n > 2), the results of researching the dependence of matrix primitivity on weight (quantity of positive elements) are presented, namely: 1) any matrix of a weight k ^ n is not primitive; 2) for k = n + 1,..., n² - n +1, there are both a not primitive matrix with weight k and a primitive matrix with weight k and exponent 7 where n+21_\/2(n - 1)J ^ 7+k ^ n² - n+3; 3) any matrix with weight k £ {n² - n+2,..., n² - 1} is primitive and its exponent 7 =2. It is shown that, for some primitive matrices, the weight is not monotonically non-decreasing function of its degree.

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