On primitivity of sets of matrices

Author: lvao

August undefined, 2024

WebAbstract. For an -tuple of nonnegative matrices , primitivity/Hurwitz primitivity means the existence of a positive product/Hurwitz product, respectively (all products are with repetitions permitted). The Hurwitz product with a Parikh vector is the sum of all products with multipliers , . Ergodicity/Hurwitz ergodicity means the existence of the corresponding … 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 Cerný conjecture. We rely on synchronizing automata theory to derive a number of results about primitive sets of matrices. Making use of an asymptotic estimate by Rystsov ...

On primitivity of sets of matrices - Semantic Scholar

Web4 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 … Web1 de nov. de 2015 · A matrix which is entrywise nonnegative is said to be primitive if every entry of is positive for some positive integer . It is well-known (see Horn & Johnson, 1995 , Corollary 8.5.9) that this is the case if and only if so the primitivity of a matrix is easy to … dusk to dawn landscape lights

The Synchronizing Probability Function for Primitive Sets of Matrices

WebThe concept of primitive sets of matrices comes up in a number of problems within the study of discrete-time switched systems. In this paper, we analyze the computational … WebMenu. Journals. SIAM Review; Multiscale Modeling & Simulation; SIAM Journal on Applied Algebra and Geometry; SIAM Journal on Applied Dynamical Systems; SIAM Journal on Applied Mathematics Web1 de nov. de 2015 · Introduction. A n × n matrix A which is entrywise nonnegative is said to be primitive if every entry of A k is positive for some positive integer k.It is well-known … cryptographic service platform

On the Degree of Nonlinearity of the Coordinate Polynomials …

On primitivity of sets of matrices - Dialnet

WebThe property of primitivity of a set of matrices is important in several applications. In particular, its presence enables one to use efﬁcient algorithms for the computation of the Lyapunov exponent of a stochastic switching system. Given a ﬁnite set of matrices M ⊂ Rn×n, one can deﬁne a stochastic switching system as: x WebBeasley 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 … dusk to dawn landscapingWebprimitivity 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 dusk to dawn lantern lights

"WebThe property of primitivity of a set of matrices is important in several applications. In particular, its presence enables one to use efﬁcient algorithms for the computation of … " - On primitivity of sets of matrices

On primitivity of sets of matrices

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 … Web1 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

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Webclosely related. Using matrix theoretic characterizations, we identify when such channels are primitive and prove that the primitivity of the channels depend on that of their associated stochastic matrices. We will also introduce the notion of the Holevo rank and find a new bound for the primitivity of the channel in terms of this rank. Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆

WebOn primitivity of sets of matrices. In Proceedings of the 47th IEEE conference on decision and control. Google Scholar; br000020 V. Blondel, A. Olshevsky, How to decide … WebInformación del artículo On primitivity of sets of matrices. Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 61, 2015, págs. 80-88 Idioma: inglés Texto completo no disponible (Saber más ...); Resumen. A nonnegative matrix AA is called primitive if AkAk is positive for some integer k>0k>0.

WebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA Web4 de abr. de 2024 · Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …

Web1 de ago. de 2024 · In our approach, we use the elements of semigroups as labels to generalize the notion of primitivity and unify theorems of Section 1. Let A = {a1, a2, . . . , ak} be a ï¬ nite set of labels. Our main idea is to treat A as elements of a semigroup. Let Aâˆ— be the free semigroup generated by A: its elements are words over A and the the ...

Web15 de nov. de 2024 · Theorem 4.5. Let Φ be an entanglement breaking channel and S be the stochastic matrix representation associated to the Holevo form Φ ( X) = ∑ k Tr ( F k X) R k. Then Φ is a primitive channel if and only if S is a primitive stochastic matrix and ∑ k R k is positive definite. dusk to dawn led barn lightWeb17 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 ... cryptographic services are enabledWebIn this paper the primitivity of a positive matrix pair (A,B) is introduced as a strict positivity constraint on the asymptotic behavior of the associated two-dimensional (2D) state … cryptographic service 重いWeb5 de ago. de 2024 · 3.1 Definition. We here introduce primitivity as a two-player probabilistic game. We fix a binary NZ-set $ \mathcal {M}=\lbrace M_1,\dots ,M_m\rbrace $ of matrix size $ n\times n $ and an integer $ t\in \mathbb {N} $, and we set D to be the directed graph associated to $ \mathcal {M}$ (see Sect. 2).We see the n vertices of D as … dusk to dawn led lights amazonWeb10 de jul. de 2024 · Deciding whether a set is primitive is a PSPACE-complete problem for sets of two matrices , while it is an NP-hard problem for sets of at least three matrices . Computing the exponent of a primitive set is usually hard, namely it is an FP $^{\text {NP}[\log ]}$ -complete problem [ 15 ]; for the complexity of other problems related to … cryptographic service provider windows 11WebBlondel, 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 . dusk to dawn led fixturesWebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the … dusk to dawn led outdoor light bulb