On matrix powers in max-algebra

  title={On matrix powers in max-algebra},
  author={P. Butkovi and Raymond A. Cuninghame-Green},
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… CONTINUE READING

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