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

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

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 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 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 did albert einstein really say insanity

Generalized primitivity of labeled digraphs - ScienceDirect

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

[1306.0729] On Primitivity of Sets of Matrices - arXiv.org

(PDF) Locally imprimitive points on elliptic curves - ResearchGate

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 … 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 … did albert einstein know how to driveWebLet 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 ... did albert einstein make the atomic bomb

"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 … " - On primitivity of sets of matrices

On primitivity of sets of matrices

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 … 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 …

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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 ... 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 ...

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). 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.

Web15 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. 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 …

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 …

WebRecently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we strengthen these links by providing … did albert einstein say if you judge a fishWeb1 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 ... city gas singapore contactWeb10 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 … did albert ellis have children did albert einstein have kids with his cousinWeb10 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 . … did albert einstein married his cousinWeb23 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). city gas share priceWeb4 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 … city gas stove