On primitivity of sets of matrices

Author: qgij

August undefined, 2024

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). 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 …

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WebA nonnegative matrix A is called primitive if Ak is positive for some integer k>0. A generalization of this concept to finite sets of matrices is as follows: a set of matrices \\@fontswitchM={A1,A2,…,Am} is primitive if Ai1Ai2…Aik is positive for some indices i1,i2,...,ik. The concept of primitive sets of matrices comes up in a number of problems … 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 grandview east 101

Local primitivity of matrices and graphs SpringerLink

WebA nonnegative matrix A is called primitive if A k is positive for some integer k > 0. A generalization of this concept to sets of matrices is as follows: A set of matrices M= {A 1,A 2, . . . ,A m} is primitive if A i1 A i2. . .A ik is positive for some indices i 1, i 2, ..., i k,.The concept of primitive sets of matrices is of importance in several applications, including … 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 ... 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 grandview east condominiums

Entanglement breaking channels, stochastic matrices, and primitivity ...

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WebSearch 207,218,109 papers from all fields of science. Search 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. grandview east condosWebLet 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 ... chinese style green beans with garlic

"WebOn primitivity of sets of matrices @article{Blondel2013OnPO, title={On primitivity of sets of matrices}, author={Vincent D. Blondel and Rapha{\"e}l M. Jungers and … " - On primitivity of sets of matrices

On primitivity of sets of matrices

In Memory of Academician Marius Iosifescu arXiv:2304.05227v1 …

WebGiven a square matrix A over the integers, we consider the Z-module M A generated by the set of all matrices that are permutation-similar to A.Motivated by analogous problems on signed graph decompositions and block designs, we are interested in the completely symmetric matrices a I + b J belonging to M A.We give a relatively fast method to … 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 ...

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WebRecently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we strengthen these links by providing … 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.

WebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). Web4 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 …

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. 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

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 …

Web25 de fev. de 2024 · B. Liu, “Generalized Exponents of Boolean Matrices,” Linear Algebra Appl. 373, 169–182 (2003). Article MathSciNet MATH Google Scholar Z. Miao and K. Zhang, “The Local Exponent Sets of Primitive Digraphs,” Linear … chinese style hair accessoriesWeb17 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 ... chinese style lamp sketchupWebMenu. Journals. SIAM Review; Multiscale Modeling & Simulation; SIAM Journal on Applied Algebra and Geometry; SIAM Journal on Applied Dynamical Systems; SIAM Journal on Applied Mathematics chinese style ladies jacketsWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 chinese style lightingWebInformación 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. chinese style home decorWeb4 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 … grandview east condo panama city beachWebThe 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 … grandview east london