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On primitivity of sets of matrices

Web23 de ago. de 2024 · The article surveys the main results on the primitivity and local primitivity of digraphs and matrices from the inception of this research area in 1912 by now. ... Ya. E. Avezova, “On Primitivity of Some Sets of Shift Registers Mixing Digraphs,” Prikl. Diskretn. Mat. Prilozh. No. 10, 60–62 (2024). WebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the …

On primitivity of sets of matrices IEEE Conference Publication

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 ... 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 … bio service nord friesoythe https://stephaniehoffpauir.com

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

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 … 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 … WebSearch 207,218,109 papers from all fields of science. Search bioservice handel

Primitivity of Positive Matrix Pairs: Algebraic Characterization, …

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On primitivity of sets of matrices

Primitive Matrices with Combinatorial Properties

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. 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 …

On primitivity of sets of matrices

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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 … 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 …

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 … 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 …

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 …

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 …

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 bioservice solutionsWebThe 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 biosesang 5x sds-page loading bufferWeb25 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 … bioset instituteWeb1 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, . . . … bio service hammWebprimitivity 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 dairyland computers and consultingWebThe 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 … dairyland claims phoneWeb10 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 . … dairyland company