On primitivity of sets of matrices

Author: ahws

August undefined, 2024

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 ... 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 …

On primitivity of sets of matrices - Semantic Scholar

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 … 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). phosphorescence book julia baird

Prove Matrix is Primitive - Mathematics Stack Exchange

WebLet 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 ... 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 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 … how does acetylcholine affect heart rate

The Synchronizing Probability Function for Primitive Sets of Matrices

Primitivity and Hurwitz primitivity of nonnegative matrix tuples: …

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 … 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 how does acetylcholine affect the brainWebWe 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 ... how does ace inhibitor cause angioedema

"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 … " - On primitivity of sets of matrices

On primitivity of sets of matrices

Primitivity and Hurwitz Primitivity of Nonnegative Matrix …

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. Web25 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 …

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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. Webpositive matrix/matrices on partitions (of the column index sets)” — this corresponds to the general case from Deﬁnition 2.11 — and “[∆]-positive matrix/matrices” — this corresponds to the special case from Deﬁnition 2.11. For generic names based on Deﬁnition 2.12, we proceed similarly.

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 … 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 …

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 …

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 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, . . . … phosphorescence examples in naturehttp://zhuyinfeng.org/Data/Preprints/Hurwitz221103.pdf phosphorescence julia baird summaryWeb17 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 ... phosphorescence intersystem crossingWebprimitivity 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 phosphorescence julia baird reviewWebBeasley 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 … phosphorescence lifetime imagingWebA 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 … phosphorescence lifetime imaging microscopyWebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the … how does aceu aim so well