共查询到20条相似文献,搜索用时 15 毫秒
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Derek. K. Chang 《Linear and Multilinear Algebra》2013,61(3-4):313-317
For n 3 and sufficiently small a 0, the minimum value of the permanent function restricted on n × n doubly stochastic matrices with at least one entry equal to a is obtained. For n = 3, the explicit form of the function p is derived where p(a) = min{per(C):C = (cij )?Ω3 c 11 = a}a? [0, 1]. 相似文献
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John Brian Burghduff 《Linear and Multilinear Algebra》1995,40(2):125-140
The permanent function on the set of n×n doubly stochastic matrices with zero main diagonal attains a strict local minimum at the matrix whose off diagonal entries are all equal to 1/(n-1). 相似文献
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Henryk Minc 《Linear and Multilinear Algebra》1984,15(3):225-243
A study of properties of matrices with minimum permanent in a face of the polyhedron of doubly stochastic n × n matrices. The minima are determined for certain faces. 相似文献
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Henryk Minc 《Linear and Multilinear Algebra》1975,3(1):91-94
It is shown that if all subpermaneats of order k of an n × n doubly stochastic matrix are equal for some k ≤ n - 2, then all the entries of the matrix must be equal to 1/n. 相似文献
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It is shown that the minimum value of the permanent on the n× ndoubly stochastic matrices which contain at least one zero entry is achieved at those matrices nearest to Jnin Euclidean norm, where Jnis the n× nmatrix each of whose entries is n-1. In case n ≠ 3 the minimum permanent is achieved only at those matrices nearest Jn; for n= 3 it is achieved at other matrices containing one or more zero entries as well. 相似文献
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EVA Achilles 《Linear and Multilinear Algebra》1977,5(1):63-70
The doubly stochastic matrices with a given zero pattern which are closest in Euclidean norm to Jnn, the matrix with each entry equal to 1/n, are identified. If the permanent is restricted to matrices having a given zero pattern confined to one row or to one column, the permanent achieves a local minimum at those matrices with that zero pattern which are closest to Jnn. This need no longer be true if the zeros lie in more than one row or column. 相似文献
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Richard Sinkhorn 《Linear and Multilinear Algebra》1976,4(3):201-203
The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined. 相似文献
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Richard Sinkhorn 《Linear and Multilinear Algebra》2013,61(3):201-203
The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined. 相似文献
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The tridiagonal Birkhoff polytope, , is the set of real square matrices with nonnegative entries and all rows and columns sums equal to 1 that are tridiagonal. This polytope arises in many problems of enumerative combinatorics, statistics, combinatorial optimization, etc. In this paper, for a given a p-face of , we determine the number of faces of lower dimension that are contained in it and we discuss its nature. In fact, a 2-face of is a triangle or a quadrilateral and the cells can only be tetrahedrons, pentahedrons or hexahedrons. 相似文献
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Richard A. Brualdi 《Linear and Multilinear Algebra》2013,61(3):393-408
We consider a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0,?1]. This class generalizes the class of doubly stochastic matrices. We investigate the corresponding polytope Ω(b|c) of such matrices. Main results include a generalization of the Birkhoff–von Neumann theorem and a characterization of the faces, including edges, of Ω(b|c). 相似文献
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Let pk(A), k=2,…,n, denote the sum of the permanents of all k×k submatrices of the n×n matrix A. A conjecture of Ðokovi?, which is stronger than the famed van der Waerden permanent conjecture, asserts that the functions pk((1?θ)Jn+;θA), k=2,…, n, are strictly increasing in the interval 0?θ?1 for every doubly stochastic matrix A. Here Jn is the n×n matrix all whose entries are equal . In the present paper it is proved that the conjecture holds true for the circulant matrices A=αIn+ βPn, α, β?0, α+;β=1, and , where In and Pn are respectively the n×n identify matrix and the n×n permutation matrix with 1's in positions (1,2), (2,3),…, (n?1, n), (n, 1). 相似文献
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The existence of even or odd diagonals in doubly stochastic matrices depends on the number of positive elements in the matrix. The optimal general lower bound in order to guarantee the existence of such diagonals is determined, as well as their minimal number for given number of positive elements. The results are related to the characterization of even doubly stochastic matrices in connection with Birkhoff's algorithm. 相似文献
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John Goldwasser 《Linear and Multilinear Algebra》2013,61(3-4):185-188
Let Ωn be the set of all n × n doubly stochastic matrices, let Jn be the n × n matrix all of whose entries are 1/n and let σ k (A) denote the sum of the permanent of all k × k submatrices of A. It has been conjectured that if A ε Ω n and A ≠ JJ then gA,k (θ) ? σ k ((1 θ)Jn 1 θA) is strictly increasing on [0,1] for k = 2,3,…,n. We show that if A = A 1 ⊕ ⊕At (t ≥ 2) is an n × n matrix where Ai for i = 1,2, …,t, and if for each i gAi,ki (θ) is non-decreasing on [0.1] for kt = 2,3,…,ni , then gA,k (θ) is strictly increasing on [0,1] for k = 2,3,…,n. 相似文献
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Bassam Mourad 《Linear and Multilinear Algebra》2013,61(2):99-113
In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented. 相似文献
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Bassam Mourad 《Linear and Multilinear Algebra》2004,52(2):99-113
In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented. 相似文献
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Giovanni Resta 《Linear algebra and its applications》2006,418(1):33-43
Starting from recent formulas for calculating the permanents of some sparse circulant matrices, we obtain more general formulas expressing the permanents of a wider class of matrices as a linear combination of appropriate determinants. 相似文献