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 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
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.
