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On Spectral Properties of Doubly Stochastic Matrices [PDF]
Symmetry, 2020 The relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems, concerning the spectral properties of doubly stochastic matrices.
Javed Hussain +2 more
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Doubly stochastic and combined matrices [PDF]
Linear and Multilinear Algebra[EN] In this work, doubly stochastic combined matrices are studied. The combined matrix is known as Relative Gain Array in control theory. In particular, the characterization of all matrices such that their combined matrix is doubly stochastic is studied for real matrices of order 3.
Ana Maria Urbano +2 more
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A characterization of even doubly-stochastic matrices [PDF]
Discrete Mathematics, 2009 A doubly-stochastic square matrix is even if it is a convex combination of even permutation matrices. The authors obtain a characterization of an even doubly-stochastic matrix by the even diagonals contained in the matrix.
Joachim Von Below
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Doubly stochastic matrices of trees [PDF]
Applied Mathematics Letters, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao-Dong Zhang 0001, Jia-Xi Wu
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Doubly stochastic matrices and the Bruhat order [PDF]
Czechoslovak Mathematical Journal, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brualdi, Richard A. +2 more
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Frobenius normal forms of doubly stochastic matrices [PDF]
Special Matrices, 2019 An elementary proof of a fundamental result on doubly stochastic matrices in Frobenius normal form is given. This result is used to establish several well-known results concerning permutations, including a theorem due to ...
Paparella Pietro
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Permanents of doubly stochastic matrices [PDF]
Discrete Mathematics, 1986 Let \(\mu_ k(n)\) denote the minimum value of the permanent of all \(n\times n\) (0,1) matrices whose row and column sums equal k. It has been conjectured that \[ \lim_{n\to \infty}[\mu_ k(n)]^{1/n}=(k-1)^{k- 1}/k^{k-2}. \] The author shows that if \(\prod^{n}_{j=1}\sum^{n}_{i=1}a_{ij}\prod_{k\neq 1}(1- a_{kj})\leq per A\) for any \(n\times n\) doubly ...
Chang, Derek K.
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An inequality for doubly stochastic matrices [PDF]
Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, 1976 Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE
Johnson, Charles R., Kellogg, R. Bruce
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The polytope of even doubly stochastic matrices [PDF]
Journal of Combinatorial Theory, Series A, 1991 An even doubly stochastic matrix is even if it is the convex combination of even permutation matrices. This paper studies the combinatorial structure of the polytope of these matrices of a fixed order \(n\). For \(n\geq 4\) the dimension is \((n-1)^ 2\). Five families of valid independent inequalities (necessary conditions) and one sufficient condition
Richard A. Brualdi, Bolian Liu
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Extreme symmetric doubly stochastic matrices [PDF]
Journal of Combinatorial Theory, Series A, 1980 AbstractWe characterize the extreme points of the polytope of symmetric doubly stochastic matrices of a given arbitrary order.
Aharoni, Ron
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