in probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})}...

summing to 1 (so it is also called a column stochastic matrix). A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row...

Doubly stochastic may refer to: Doubly stochastic model Doubly stochastic matrix This disambiguation page lists articles associated with the title Doubly...

An n × n matrix P is doubly stochastic precisely if both P and its transpose PT are stochastic matrices. A stochastic matrix is a square matrix of nonnegative...

covariance matrix. Doubly stochastic matrix — a non-negative matrix such that each row and each column sums to 1 (thus the matrix is both left stochastic and...

of non-negative matrices, e.g. stochastic matrix; doubly stochastic matrix; symmetric non-negative matrix. Metzler matrix Berman, Abraham; Plemmons, Robert...

constant will yield a doubly stochastic matrix, whose row sums and column sums equal to unity. However, unlike the doubly stochastic matrix, the diagonal sums...

are denoted A and B is a doubly stochastic matrix D such that DA = BD. If the doubly stochastic matrix is a permutation matrix, then it constitutes a graph...

{\displaystyle R_{\pi }} . Every permutation matrix is doubly stochastic. The set of all doubly stochastic matrices is called the Birkhoff polytope, and...

Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any doubly stochastic matrix. 1985: Jozsef Beck for tight bounds...

polytope are the permutation matrices, and therefore that any doubly stochastic matrix may be represented as a convex combination of permutation matrices;...

and sum up to one. Stochastic matrices are used to define Markov chains with finitely many states. A row of the stochastic matrix gives the probability...

orthostochastic matrix is a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some orthogonal matrix. The detailed...

In mathematics, a unistochastic matrix (also called unitary-stochastic) is a doubly stochastic matrix whose entries are the squares of the absolute values...

square real matrix A with strictly positive elements. Decomposition: A = D 1 S D 2 {\displaystyle A=D_{1}SD_{2}} , where S is doubly stochastic and D1 and...

diagonal elements such that D1AD2 is doubly stochastic. The matrices D1 and D2 are unique modulo multiplying the first matrix by a positive number and dividing...

Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any doubly stochastic matrix. Egorychev is now a professor in...

conjectured that the minimum permanent among all n × n doubly stochastic matrices is n!/nn, achieved by the matrix for which all entries are equal to 1/n. Proofs...

_{j}(\log q_{j})P_{ij}),} where Pi j = |vi*wj|2. Since the matrix (Pi j)i j is a doubly stochastic matrix and -log is a convex function, the above expression...

lottery on deterministic allocations. A bistochastic matrix (also called: doubly-stochastic) is a matrix in which all elements are greater than or equal to...

probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled...

for existence is similar with Birkhoff–von Neumann theorem for doubly stochastic matrix. Here is an example that illustrates the existence and non-uniqueness...

result due to Sinkhorn, which states that a doubly stochastic matrix is obtained from any square matrix with all positive entries by the iterative process...

represent every n × n {\displaystyle n\times n} doubly stochastic matrix, and that some doubly stochastic matrices need this many permutation matrices....

entries, see Perron–Frobenius theorem. Doubly stochastic matrix Hurwitz-stable matrix Joel Lee Brenner Metzler matrix Muirhead's inequality Bendixson's inequality...

{\displaystyle \mathbf {x} =\mathbf {D} \mathbf {y} } for some doubly stochastic matrix D {\displaystyle \mathbf {D} } .: Thm. 2.1  In particular, x {\displaystyle...

Marvin; Newman, Morris (1959). "On the minimum of the permanent of a doubly stochastic matrix". Duke Mathematical Journal. 26. doi:10.1215/S0012-7094-59-02606-7...

Stochastic equicontinuity Stochastic gradient descent Stochastic grammar Stochastic investment model Stochastic kernel estimation Stochastic matrix Stochastic...

from each other. The result relies on the observation that every doubly stochastic matrix is the convex hull of permutation matrices. For the Operations...

perfect fractional matching, then the matrix representation of M {\displaystyle M} is a doubly stochastic matrix – the sum of elements in each row and...