منابع مشابه
On matrix powers in max-algebra
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 proble...
متن کاملCsr Expansions of Matrix Powers in Max Algebra
We study the behavior of max-algebraic powers of a reducible nonnegative matrix A ∈ Rn×n + . We show that for t ≥ 3n2, the powers At can be expanded in max-algebraic sums of terms of the form CStR, where C and R are extracted from columns and rows of certain Kleene stars, and S is diagonally similar to a Boolean matrix. We study the properties of individual terms and show that all terms, for a ...
متن کاملOn the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra
If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, “On the sequence of consecutive matrix powers of boolean matrices in the max-plus algebra,” in Theory and Practice of Control and Systems (Proceedings of the 6th IEEE Mediterranean Conference on Control and Systems, Alghero, Italy, June 1998) (A. Tornambè, G. Conte, and A.M. Perdon, eds.)...
متن کاملMatrix period in max-drast fuzzy algebra
Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...
متن کاملOn the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra
We study the sequence of consecutive powers of a matrix in the max-plus algebra, which has maximum and addition as its basic operations. If the matrix is irreducible then it is well known that the ultimate behavior of the sequence is cyclic. For reducible matrices the ultimate behavior is more complex, but it is also cyclic in nature. We will give a detailed characterization of the rates and pe...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.09.027