doubly stochastic matrixの例文

例文

1. A permutation matrix is itself a doubly stochastic matrix, but it also plays a special role in the theory of these matrices.
2. Since U is a unitary matrix, S is a doubly stochastic matrix and we have \ tilde { a } = S \ tilde { \ lambda }.
3. Thus, a doubly stochastic matrix is a square matrix of nonnegative real entries in which the sum of the entries in each row and the sum of the entries in each column is 1.
4. He obtained a tightening of the Birkhoff von Neumann theorem with H . K . Farahat stating that every doubly stochastic matrix can be obtained as a convex combination of spectra of doubly stochastic matrices.
5. To satisfy the constraints, it is possible to use a 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 of alternating row and column normalizations.