In mathematics, especially in probability and combinatorics, a doubly stochastic matrix (also called bistochastic), is a square matrix of nonnegative real numbers, each of whose rows and columns sum to 1, i.e.,
- ,
Thus, a doubly stochastic matrix is both left stochastic and right stochastic.
Such a transition matrix is necessarily a square matrix: if every row sums to one then the sum of all entries in the matrix must be equal to the number of rows, and since the same holds for columns, the number of rows and columns must be equal.
Read more about Doubly Stochastic Matrix: Birkhoff Polytope and Birkhoff–von Neumann Theorem, Other Properties
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