On primitivity of sets of matrices
WebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). Webtheir names. Mimicking their terminology, we call the exponent of a primitive set Mthe length of its shortest positive product, and we indicate it by exp(M). The primitivity property of nonnegative matrix sets has lately found applica-tions in various elds as in consensus of discrete-time multi-agent systems [7], in
On primitivity of sets of matrices
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WebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA WebWe pay special attention to the set of matrices without zero rows and columns, denoted by $\mathscr{NZ}$, due to its intriguing connections to the Černý conjecture. We rely on synchronizing automata theory to derive a number of …
WebThe property of primitivity ofa set of matrices is impor-tant in several applications. In particular, its presence enables one to use efficient algorithms for the computa-tion of … Web8 de set. de 2024 · ularly of interest as, while testing the primitivity of a NZ-set of m matrices is polynomial in nm ([21], Proposition 2), finding its exp onent is computationally hard ([13], Theorem 12).
Web17 de mai. de 2024 · Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding \v{C}ern\'{y} conjecture by studying the primitivity ... WebIn this paper, we analyze the computational complexity of deciding if a given set of matrices is primitive and we derive bounds on the length of the shortest positive product. We show …
Web8 de abr. de 2024 · corresponding sets of primes S K,x, S E /K, and S E/K,P o f K in terms of the splitting behaviour of their elements p in suitable e xtensions K ⊂ K ℓ , with ℓ ranging over all prime numbers.
Webprimitivity of one matrix (see, for instance [12, chapter 8]). However, for a set of matrices A 1 ,...,A k the situation is more difficult: instead of working with powers of one matrix, we artema samba 5fWebBeasley and A.E. Guterman , The characterization of operators preserving primitivity for matrix k-tuples, Linear Algebra Appl., 430 ( 2009), pp. 1762 -- 1777 . ... On primitivity of … artem arutyunyanWebBlondel, Vincent [UCL] Jungers, Raphaël M. [UCL] olshevsky, Alex [University of Illinois at Urbana–Champaign, USA] . A nonnegative matrix is called primitive if is positive for some integer . A generalization by Protasov and Voynov (2012) of this concept to finite sets of matrices is as follows: a set of matrices is primitive if is positive for some indices . artemarmol santa martaWeb1 de jan. de 2013 · Check if you have access through your login credentials or your institution to get full access on this article. Sign in artema samba 3fWeb4 de jun. de 2013 · On the other hand, defining ${\mathcal P}$ to be the set of matrices with no zero rows or columns, we give a simple combinatorial proof of a previously … arte marziale yangWebLet start with F(1) = {2} because the first row in the matrix T, the second column is positive. F(5) = {1,2} as you see in the matrix T in the fifth row, the first and the second column are positive. F2(1) = {3} because in the matrix T2 in the first row, the third column is positive. F3(3) = {1,2} if you see the matrix T3 in the third row ... artema samba 3f a45680staWeb4 de jun. de 2013 · In this paper, we analyze the computational complexity of deciding if a given set of matrices is primitive and we derive bounds on the length of the shortest … artema sahibi kim