Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599561 | Linear Algebra and its Applications | 2014 | 15 Pages |
Abstract
Each Markov interval map f naturally produces a transition 0–1 matrix of interval type (in every row, the entries equal to 1 should be consecutive). We show that any 0–1 matrix A can be transformed into an interval type matrix AIAI, by a careful use of the state splitting. We then prove that AIAI can be realized as a transition matrix of an interval map fAI,λAIfAI,λAI arising from the Perron–Frobenius eigenvalue λAIλAI and eigenvector of AIAI. Finally, we construct orbit representations associated with A from those of AIAI arising from the dynamical system ([0,1],fAI,λAI)([0,1],fAI,λAI).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
C. Correia Ramos, Nuno Martins, Paulo R. Pinto,