On primitivity of sets of matrices

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August undefined, 2024

WebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA Web1 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.

Classification of $k$-Primitive Sets of Matrices SIAM Journal on ...

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. 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 iron mountain work from home

On primitivity of sets of matrices - ScienceDirect

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

On primitivity of sets of matrices IEEE Conference Publication

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. 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 … iron mountain windsor ctWebGiven 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 … port orford heads trail

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On primitivity of sets of matrices

In Memory of Academician Marius Iosifescu arXiv:2304.05227v1 …

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 … WebIn 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 …

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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 … 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

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 ... Web11 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 =

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 ... 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).

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

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 … port orford heads state parkWebThe 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 iron mountain winter michael t. ribbleWebThe 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 … iron mountain yacht clubWeb15 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. port orford heads state park oregonWebLet 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 ... port orford historyWebOn 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 … iron mountain zip code michiganWebtheir 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 port orford homes for rent