On matrix powers in max-algebra
نویسندگان
چکیده
Let A = (aij ) ∈ Rn×n,N = {1, . . . , n} and DA be the digraph (N, {(i, j); aij > −∞}). The matrix A is called irreducible if DA is strongly connected, and strongly irreducible if every maxalgebraic power of A is irreducible. A is called robust if for every x with at least one finite component, A(k) ⊗ x is an eigenvector of A for some natural number k. We study the eigenvalue–eigenvector problem for powers of irreducible matrices. This enables us to characterise robust irreducible matrices. In particular, robust strongly irreducible matrices are described in terms of eigenspaces of matrix powers. © 2006 Elsevier Inc. All rights reserved. AMS classification: 15A18
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