… We also prove in Section 3 that for primitive sets of matrices in P , the shortest positive product
has length O ( n 3 ) . Moreover, we show that in this case the length of the shortest positive …

… on the primitivity of matrices (digraphs) and generalizations of this property; the theoretical
foundations of the matrix… the main results on the primitivity of digraphs and matrices and give …

… hj depends substantially on xi. The adjacency … of primitivity and exponent, we introduce
and examine the notions of the local primitivity and the local exponents of a nonnegative matrix (…

… a set of k nonnegative matrices is either k-primitive or there exists a nontrivial partition of the
set of basis vectors, on which these matrices act as … classification of k-primitive families and a …

… result on primitive sets of matrices having total support. We plan to apply our ideas to the
closely related concept of scrambling matrix and its generalizations to sets of matrices as well. …

… on the exponent of a primitive graph In this section the theorems on the gaps in the exponent
setof n by n primitive matrices … The theorem is based on a few preliminary remarks. Remark …

… primitive vector \(\alpha\) of weight \(\sum_{i=1}^m\alpha_i=O(n^3)\). We also report results
on ergodic and Hurwitz ergodic matrix … We improve on this work by presenting a primitivity …

… In Markov chain theory, regular chain is one whose transition matrix is a primitive matrix. …
In this paper we discuss various results on the notion of k-primitivity. Before further continuation, …

… Our primitivity algorithm takes as input a generating set for a … but here we focus on its
application to primitivity testing. Assume that the matrix group G acts absolutely irreducibly on the Ž . …

… and primitivity of a nonnegative matrix depend on only the graph of that matrix rather than …
It is possible to express graphic properties in terms of Boolean relation matrices, ie matrices …