We develop a new approach for characterizing k-primitive matrix families. Such families generalize the notion of a primitive matrix. They have been intensively studied in the recent literature due to applications to Markov chains, linear dynamical systems, and graph theory. We prove, under some mild assumptions, that 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 commuting permutations. This gives a convenient classification of k-primitive families and a polynomial-time algorithm to recognize them. This also extends some results of Perron-Frobenius theory to nonnegative matrix families. Copyright © 2013 by SIAM.
|Titolo:||Classification of k-primitive sets of matrices|
|Autori interni:||PROTASOV, Vladimir|
|Data di pubblicazione:||2013|
|Rivista:||SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS|
|Appare nelle tipologie:||1.1 Articolo in rivista|