Upper generalized exponents of two-colored primitive extremal ministrong digraphs
A two-colored digraph is a digraph each of whose arcs is colored by red or blue. An (h, k)-
walk in a two-colored digraph is a walk consisting of h red arcs and k blue arcs. A two …
walk in a two-colored digraph is a walk consisting of h red arcs and k blue arcs. A two …
Exponents of nonnegative matrix pairs
The notions of primitivity and exponent of a square nonnegative matrix A are classical: A is
primitive provided there is a nonnegative integer k such that Ak is entrywise positive and in …
primitive provided there is a nonnegative integer k such that Ak is entrywise positive and in …
Sets of nonnegative matrices without positive products
VY Protasov, AS Voynov - Linear Algebra and its Applications, 2012 - Elsevier
For an arbitrary irreducible set of nonnegative d× d-matrices, we consider the following
problem: does there exist a strictly positive product (with repetitions permitted) of those …
problem: does there exist a strictly positive product (with repetitions permitted) of those …
Primitive sets of nonnegative matrices and synchronizing automata
A set of nonnegative matrices M={M_1,M_2,...,M_k\} is called primitive if there exist possibly
equal indices i_1,i_2,...,i_m such that M_i_1M_i_2⋯M_i_m is entrywise positive. The length …
equal indices i_1,i_2,...,i_m such that M_i_1M_i_2⋯M_i_m is entrywise positive. The length …
Controllability and reachability of 2-D positive systems: a graph theoretic approach
When dealing with two-dimensional (2-D) discrete state-space models, controllability
properties are introduced in two different forms: a local form, which refers to single local …
properties are introduced in two different forms: a local form, which refers to single local …
Exponents of two-colored digraphs with two cycles
Y Gao, Y Shao - Linear algebra and its applications, 2005 - Elsevier
For two nonnegative matrices A and B of the same order, the pair (A, B) is primitive if there
exist nonnegative integers h and k such that the sum of all products formed by words …
exist nonnegative integers h and k such that the sum of all products formed by words …
Exponents of a class of two-colored digraphs
Y Shao, Y Gao, L Sun - Linear and Multilinear Algebra, 2005 - Taylor & Francis
A two-colored digraph D is primitive if there exist nonnegative integers h and k with h+ k> 0
such that for each pair (i, j) of vertices there exists an (h, k)-walk in D from i to j. The exponent …
such that for each pair (i, j) of vertices there exists an (h, k)-walk in D from i to j. The exponent …
Parallel digraphs-building algorithm for polynomial realisations
In this paper, the new method of the determination of entries of the state matrices of the
positive two-dimensional systems described by the second Fornasini-Marchesini model (IIF …
positive two-dimensional systems described by the second Fornasini-Marchesini model (IIF …
Generalized exponents of primitive two-colored digraphs
Y Gao, Y Shao - Linear algebra and its applications, 2009 - Elsevier
A l-colored digraph D (l) is primitive if there exists a nonnegative integer vector α such that
for each ordered pair of vertices x and y (not necessarily distinct), there exists an α-walk in D …
for each ordered pair of vertices x and y (not necessarily distinct), there exists an α-walk in D …
Exponents of tuples of nonnegative matrices
The notions of irreducibility, primitivity, and exponent of a nonegative matrix are generalized
to k-tuples of non-negative matrices of the same order. It is shown that for each positive …
to k-tuples of non-negative matrices of the same order. It is shown that for each positive …