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 
formula_4 such that 
formula_5
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.