共查询到20条相似文献,搜索用时 31 毫秒
1.
It has been conjectured that if A is a doubly stochastic n>× n matrix such that per A(i, j)≥perA for all i, j, then either A = Jn, then n × n matrix with each entry equal to , or, up to permutations of rows and columns, , where Pn is a full cycle permutation matrix. This conjecture is proved. 相似文献
2.
The Schur product of two n×n complex matrices A=(aij), B=(bij) is defined by A°B=(aijbij. By a result of Schur [2], the algebra of n×n matrices with Schur product and the usual addition is a commutative Banach algebra under the operator norm (the norm of the operator defined on n by the matrix). For a fixed matrix A, the norm of the operator B?A°B on this Banach algebra is called the Schur multiplier norm of A, and is denoted by ∥A∥m. It is proved here that for all unitary U (where ∥·∥ denotes the operator norm) iff A is a scalar multiple of a unitary matrix; and that ∥A∥m=∥A∥ iff there exist two permutations P, Q, a p×p (1?p?n) unitary U, an (n?p)×(n?p)1 contraction C, and a nonnegative number λ such that and this is so iff , where ā is the matrix obtained by taking entrywise conjugates of A. 相似文献
4.
Let A be a subalgebra of the full matrix algebra Mn(F), and suppose J∈A, where J is the Jordan block corresponding to xn. Let be a set of generators of A. It is shown that the graph of determines whether A is the full matrix algebra Mn(F). 相似文献
5.
Shuo-Yen Robert Li 《Journal of Combinatorial Theory, Series A》1977,23(3):341-343
We determine the maximum size of a family of subsets in {1, 2,…, n} with the property that if A1, A2, A3,… are any members of the family with , then ∪Ai = {1, 2,…, n}. 相似文献
6.
We are interested in the parallel computation of a linear mapping of n real variables by a network of computers with restricted means of communication between them and without any common memory. Let denote the algebra of n×n real matrices, and let G be the graph associated with a binary, reflexive and symmetric relation R over {1,2, …,n}. We define A matrix is said to be realizable on G if it can be expressed as a product of elements of AR. Therefore, every matrix of is realizable on G if and only if AR generates . We show that AR generates if and only if G is connected. 相似文献
7.
Luc Devroye 《Journal of multivariate analysis》1982,12(1):72-79
If X1,…,Xn are independent identically distributed Rd-valued random vectors with probability measure μ and empirical probability measure μn, and if is a subset of the Borel sets on Rd, then we show that P{supA∈|μn(A)?μ(A)|≥ε} ≤ cs(, n2)e?2n∈2, where c is an explicitly given constant, and s(, n) is the maximum over all (x1,…,xn) ∈ Rdn of the number of different sets in {{x1…,xn}∩A|A ∈}. The bound strengthens a result due to Vapnik and Chervonenkis. 相似文献
8.
József Beck 《Journal of Combinatorial Theory, Series A》1981,30(2):117-133
Let {Ai} be a family of sets and let S = ∩iAi. By a positional game we shall mean a game played by two players on {Ai}. The players alternately pick elements of S and that player wins who fist has all the elements of one of the Ai. This paper deals with almost disjoint hypergraphs only, i.e., |Ai∪Aj| ? 1 if i ≠ j. Let be the smallest integer for which there is an almost disjoint n-uniform hypergraph , so that the first player has a winning strategy. It is shown that , which was conjectured by Erdös. The same method is applied to prove a conjecture of Hales and Jewett on r-dimensional tick-tack-toe if r is large enough. Finally we prove that for an arbitrary almost disjoint n-uniform hypergraph the second player has such a strategy that the first player unable to win in his mth move if m < (2 ? ?)n. 相似文献
9.
A circular string A = (a1,…,an) is a string that has n equivalent linear representations Ai = ai,…,an,a1,…,ai?1 for i = 1,…,n. The ai's are assumed to be well ordered. We say that Ai < Aj if the word ai…ana1…ai?1 precedes the word aj…ana1…aj?1 in the lexicographic order, Ai ? Aj if either Ai < Aj or Ai = Aj. Ai0 is a minimal representation of A if Ai0 ? Ai for all 1 ≤ i ≤ n. The index i0 is called a minimal starting point (m.s.p.). In this paper we discuss the problem of finding m.s.p. of a given circular string. Our algorithm finds, in fact, all the m.s.p.'s of a given circular string A of length n by using at most comparisons. The number d denotes the difference between two successive m.s.p.'s (see Lemma 1.1) and is equal to n if A has a unique m.s.p. Our algorithm improves the result of 3n comparisons given by K. S. Booth. Only constant auxiliary storage is used. 相似文献
10.
Béla Bollobás 《Journal of Combinatorial Theory, Series A》1973,15(3):363-366
It was proved by Erdös, Ko, and Radó (Intersection theorems for systems of finite sets, Quart. J. Math. Oxford Ser.12 (1961), 313–320.) that if = {;A1,…, Al}; consists of k-subsets of a set with n > 2k elements such that Ai ∩ Aj ≠ ? for all i, j then l ? (k?1n?1). Schönheim proved that if A1, …, Al are subsets of a set S with n elements such that Ai ? Aj, Ai ∩ Aj ≠ ø and Ai ∪ Aj ≠ S for all i ≠ j then . In this note we prove a common strengthening of these results. 相似文献
11.
It is shown that if Q is a quasi-group of order n and k is moderately large, there exists a subset A of Q of size k such that if t is the least number of left translates of A needed to cover Q, then . 相似文献
12.
Let Mm,n(F) denote the space of all mXn matrices over the algebraically closed field F. A subspace of Mm,n(F), all of whose nonzero elements have rank k, is said to be essentially decomposable if there exist nonsingular mXn matrices U and V respectively such that for any element A, UAV has the form where A1 is iX(k–i) for some i?k. Theorem: If is a space of rank k matrices, then either is essentially decomposable or dim ?k+1. An example shows that the above bound on non-essentially-decomposable spaces of rank k matrices is sharp whenever n?2k–1. 相似文献
13.
Let be the Clifford algebra constructed over a quadratic n-dimensional real vector space with orthogonal basis {e1,…, en}, and e0 be the identity of . Furthermore, let Mk(Ω;) be the set of -valued functions defined in an open subset Ω of Rm+1 (1 ? m ? n) which satisfy Dkf = 0 in Ω, where D is the generalized Cauchy-Riemann operator and k? N. The aim of this paper is to characterize the dual and bidual of Mk(Ω;). It is proved that, if Mk(Ω;) is provided with the topology of uniform compact convergence, then its strong dual is topologically isomorphic to an inductive limit space of Fréchet modules, which in its turn admits Mk(Ω;) as its dual. In this way, classical results about the spaces of holomorphic functions and analytic functionals are generalized. 相似文献
14.
Mark Blondeau Hedrick 《Linear algebra and its applications》1975,10(2):177-179
The author proves that if A is a matrix at which the permanent achieves a local minimum relative to the set of n x n doubly stochastic matrices, then for aij=0, . 相似文献
15.
Let A, B be n × n matrices with entries in a field F. We say A and B satisfy property if B or Bt is diagonally similar to A. It is clear that if A and B satisfy property , then they have equal corresponding principal minors, of all orders. The question is to what extent the converse is true. There are examples which show the converse is not always true. We modify the problem slightly and give conditions on a matrix A which guarantee that if B is any matrix which has the same principal minors as A, then A and B will satisfy property . These conditions on A are formulated in terms of ranks of certain submatrices of A and the concept of irreducibility. 相似文献
16.
A subpolytope Γ of the polytope Ωn of all n×n nonnegative doubly stochastic matrices is said to be a permanental polytope if the permanent function is constant on Γ. Geometrical properties of permanental polytopes are investigated. No matrix of the form 1⊕A where A is in Ω2 is contained in any permanental polytope of Ω3 with positive dimension. There is no 3-dimensional permanental polytope of Ω3, and there is essentially a unique maximal 2-dimensional permanental polytope of Ω3 (a square of side ). Permanental polytopes of dimension are exhibited for each n?4. 相似文献
17.
We show that for a C1-dynamical system (A, G, α) with G discrete (abelian) the Connes spectrum Γ(α) is equal to if and only if every nonzero closed ideal in G × αA has a nonzero intersection with A. Denote by GJ the closed subgroup of G that leaves fixed the primitive ideal J of A. We show for a general group G that if all isotropy groups GJ are discrete, then GXαA is simple if and only if A is G-simple and . This result is applicable not only when G is discrete but also when G? or G? provided that A is not primitive. Specializing to single automorphisms (i.e., G=) we show that if (the transposed of) α acts freely on a dense set of points in , then Λ(α)=. The converse is only proved when A is of type I. 相似文献
18.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
19.
Cai Mao-cheng 《Discrete Mathematics》1984,48(1):121-123
Let S be a set of n elements, and k a fixed positive integer . Katona's problem is to determine the smallest integer m for which there exists a family = {A1, …, Am} of subsets of S with the following property: |i| ? k (i = 1, …, m), and for any ordered pair xi, xi ∈ S (i ≠ j) there is A1 ∈ such that xi ∈ A1, xj ? A1. It is given in this note that . 相似文献
20.
A Lyapunov transformation is a linear transformation on the set n of hermitian matrices H ? n,n of the form A(H) = A1H + HA, where A ?n,n. Given a positive stable A ?n,n, the Stein-Pfeffer Theorem characterizes those K ? n for which K = B(H), where B is similar to A and H is positive definite. We give a new proof of this result, and extend it in several directions. The proofs involve the idea of a controllability subspace, employed previously in this context by Snyders and Zakai. 相似文献