On nonnegative matrices
Mordechai Lewin · Pacific Journal of Mathematics · 1971
The following characterisation of totally indecomposable nonnegative ^-square matrices is introduced: A nonnegative ^-square matrix is totally indecomposable if and only if it diminishes the number of zeros of every ^-dimensional nonnegative vector which is neither positive nor zero.From this characterisation it follows quite easily that: I.The class of totally indecomposable nonnegative nsquare matrices is closed with respect to matrix multiplication.II.The in -l)-st power of a matrix of that class is positive.A very short proof of two equivalent versions of the Kόnig-Frobenius duality theorem on (0, l)-matrices is supplied at the end.