The notion of scrambling index was firstly introduced by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every pair of vertices u and v of D there exist two directed paths of lengths k to a common vertex w. This notion turned out to be useful for several applications, e. g., to estimate eigenvalues of non-negative primitive stochastic matrices. In 2010 Huang and Liu with the background of a memoryless communication system generalized this notion to λ-tuples of vertices and named it λ-th upper scrambling index. These notions can be reformulated in terms of matrix theory. A standard way to generate matrices with the given λ-th upper scrambling index is to apply certain matrix transformations that preserve this index to the existing examples of matrices with known λ-th upper scrambling index. In this paper we completely characterize bijective linear maps preserving λ-th upper scrambling index 1 or 0.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB.
Spectral properties of nonegative matrices are considered. Asymptotic stability and stabilisation problems of positive discrete-time and continous-time linear systems by feedbacks are discussed. The electric RC-networks are presented as examples of positive systems. Numerical calculations were made using the MATLAB program.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.