The extreme matrices of the doubly-nonnegative cone have some
restrictions on their ranks. This function checks to see whether the
rank ``r`` would be an admissible rank for an ``n``-by-``n`` matrix.
The extreme matrices of the doubly-nonnegative cone have some
restrictions on their ranks. This function checks to see whether the
rank ``r`` would be an admissible rank for an ``n``-by-``n`` matrix.
# can't compute the dimension of a set of matrices anyway, so we
# convert them all to vectors and just ask for the dimension of the
# resulting vector space.
# can't compute the dimension of a set of matrices anyway, so we
# convert them all to vectors and just ask for the dimension of the
# resulting vector space.
vectors = map(phi,spanning_set)
V = span(vectors, A.base_ring())
vectors = map(phi,spanning_set)
V = span(vectors, A.base_ring())
msg = 'Rank %d not possible in dimension %d.'
raise ValueError(msg % (rank, V.dimension()))
msg = 'Rank %d not possible in dimension %d.'
raise ValueError(msg % (rank, V.dimension()))