- # Normalize these with our inner product before handing them back.
- # And since we embedded them, we can drop back to the "field" that
- # we started with instead of the complex extension "F".
- return tuple( (s / _complex_hermitian_matrix_ip(s,s).sqrt()).change_ring(field)
- for s in S )
+ # Since we embedded these, we can drop back to the "field" that we
+ # started with instead of the complex extension "F".
+ S = [ s.change_ring(field) for s in S ]
+ if normalize:
+ S = [ s / _complex_hermitian_matrix_ip(s,s).sqrt() for s in S ]
+
+ return tuple(S)