Results 11 to 20 of about 1,476 (274)
Convex sets of doubly stochastic matrices [PDF]
Journal of Combinatorial Theory, Series A, 1974 AbstractLet Ω denote the set of all n by n doubly stochastic matrices and let m be a positive integer. Then the set Ωm = {A ϵ Ω : 0 ⩽ aij ⩽ 1m, 1 ⩽ i, j ≤ n} is the convex hull of the matrices in Ωm having exactly m entries equal to 1m in each row and column and the other entries equal to zero.
William Watkins, Russell Merris
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A note on multivariate majorization [PDF]
Journal of Mahani Mathematical Research, 2022 A matrix $A$ is said to be multivariate majorized by a matrix $B$, written $A\prec B$, if there exists a doubly stochastic matrix $D$ such that $A = BD$ .
Mehdi Dehghanian, Ahmad Mohammadhasani
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Diagonal sums of doubly stochastic matrices [PDF]
Linear and Multilinear Algebra, 2021 Let $Ω_n$ denote the class of $n \times n$ doubly stochastic matrices (each such matrix is entrywise nonnegative and every row and column sum is 1). We study the diagonals of matrices in $Ω_n$. The main question is: which $A \in Ω_n$ are such that the diagonals in $A$ that avoid the zeros of $A$ all have the same sum of their entries.
Richard A. Brualdi, Geir Dahl
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Positional Voting and Doubly Stochastic Matrices [PDF]
The American Mathematical Monthly, 2021 We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile.
Jacqueline Anderson +2 more
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A short note on extreme points of certain polytopes
Special Matrices, 2020 We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices.
Cao Lei, Hall Ariana, Koyuncu Selcuk
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Corrigendum to “Spectra universally realizable by doubly stochastic matrices”
Special Matrices, 2023 We correct an error in the statement and the proof of Theorem 2.1 and Corollary 2.1 in our previous study [Spec. Matrices 6 (2018), 301–309], Section 2: On nonnegative matrices similar to positive matrices.
Collao Macarena +2 more
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Channel discord and distortion
New Journal of Physics, 2021 Discord, originally notable as a signature of bipartite quantum correlation, in fact can be nonzero classically, i.e. arising from noisy measurements by one of the two parties.
Wei-Wei Zhang +2 more
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On the Volume of the Polytope of Doubly Stochastic Matrices [PDF]
Experimental Mathematics, 1999 We study the calculation of the volume of the polytope B_n of n by n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices.
Chan, Clara S., Robbins, David P.
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The complete positivity of symmetric tridiagonal and pentadiagonal matrices
Special Matrices, 2022 We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix AA is completely positive. Our decomposition can be applied to a wide range of matrices.
Cao Lei, McLaren Darian, Plosker Sarah
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Convergence of an accelerated distributed optimisation algorithm over time‐varying directed networks
IET Control Theory & Applications, 2021 In this article, studying distributed optimisation over time‐varying directed networks where a group of agents aims at cooperatively minimising a sum of local objective functions is focused on.
Jinhui Hu +5 more
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