On primitivity of sets of matrices

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August undefined, 2024

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 … Web10 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 …

Classification of k-Primitive Sets of Matrices Semantic Scholar

WebSearch 207,218,109 papers from all fields of science. Search 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 … philippines relationship with russia

Primitivity and Hurwitz Primitivity of Nonnegative Matrix …

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 contains the set of stochastic matrices while NZ 2 contains the set of doubly 101 stochastic matrices. 102 A matrix is an automaton matrix if it is a zero-one matrix each row of which 103 contains a unique one. We denote by A the set of all automaton matrices, which is 104 an important subclass of NZ 1. An automaton of size nis a subset of ... 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 ... philippines regained the independence in 1945

SIAM Journal on Matrix Analysis and Applications

On primitivity of sets of matrices Automatica (Journal of IFAC)

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 … WebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the … philippines relationship with us trunking with clips

"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 … " - On primitivity of sets of matrices

On primitivity of sets of matrices

The Synchronizing Probability Function for Primitive Sets of Matrices ...

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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WebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). Webpositive matrix/matrices on partitions (of the column index sets)” — this corresponds to the general case from Deﬁnition 2.11 — and “[∆]-positive matrix/matrices” — this corresponds to the special case from Deﬁnition 2.11. For generic names based on Deﬁnition 2.12, we proceed similarly.

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 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

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 … WebBlondel, 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 .

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 …

http://zhuyinfeng.org/Data/Preprints/Hurwitz221103.pdf trunking with coverWeb25 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 … philippines rejects chinaWeb开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 philippines regular and special holidayWebclosely 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. philippines remote jobs red hatWebLet 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 ... philippines relationship with chinaWebThe 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 … trunking whiteWebThe 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 trunking with sockets