On primitivity of sets of matrices
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 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 . …
On primitivity of sets of matrices
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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 … 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 .
WebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the … 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
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, . . . … 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 …
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 …
WebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA how to ship dangerous goodsWeb17 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 ... nottage playwrightWebUpload an image to customize your repository’s social media preview. Images should be at least 640×320px (1280×640px for best display). nottage primary school bridgendWeb5 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 … nottage houseWeb15 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 to ship custard piesWebThe 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 nottage primary school holidaysWebA 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 … how to ship cutco knives for sharpening