Orthostochastic matrix

In mathematics, an 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 definition is as follows. A square matrix B of size n is doubly stochastic (or bistochastic) if all its rows and columns sum to 1 and all its entries are nonnegative real numbers. It is orthostochastic if there exists an orthogonal matrix O such that All 2-by-2 doubly stochastic matrices are orthostochastic (and also unistochastic) since for any we find the corresponding orthogonal matrix with such that For larger n the sets of bistochastic matrices includes the set of unistochastic matrices, which includes the set of orthostochastic matrices and these inclusion relations are proper.