On primitivity of sets of matrices

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August undefined, 2024

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 … 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 ...

Classi cation of k-primitive sets of matrices - ResearchGate

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 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 ... how can you improve public speaking skills

On primitivity of sets of matrices - ScienceDirect

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 … 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 … 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. how can you improve endurance

The Synchronizing Probability Function for Primitive Sets of …

Primitive sets of nonnegative matrices and synchronizing automata

WebRecently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we strengthen these links by providing … 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 … how can you improve soil healthWeb15 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. how can you improve performance management

"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 … " - On primitivity of sets of matrices

On primitivity of sets of matrices

Primitive sets of nonnegative matrices and synchronizing automata

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

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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 … 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 …

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. 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 …

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 … 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 …

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 …

http://zhuyinfeng.org/Data/Preprints/Hurwitz221103.pdf how can you improve our societyWeb1 de out. de 2024 · These notions, which include the primitivity and the local primitivity of nonnegative matrices and digraphs etc., have an important applied meaning for the study of the properties of sets of transformations of a vector space connected with essential variables and different kinds of nonlinearity. how can you improve oxygen in your bloodWeb4 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 … how can you improve sales lead generationWebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA how can you improve soilWebA 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 … how many people use badlion clientWeb11 de abr. de 2024 · sets and the Fibonacci sequence, we in troduce Schreier multisets and connect these multisets with the s -step Fibonacci sequences, deﬁned, for each s > 2 , as: F ( s ) 2 − s = how many people use bakkesmodWeb10 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 . … how many people use bandlab