gistfile1.txt

diff --git a/python/firedrake/nullspace.py b/python/firedrake/nullspace.py
index 382f039..0daf197 100644
--- a/python/firedrake/nullspace.py
+++ b/python/firedrake/nullspace.py
@@ -1,5 +1,5 @@
 from petsc4py import PETSc
-from types import IndexedFunctionSpace
+from types import IndexedFunctionSpace, Function
 
 
 class VectorSpaceBasis(object):
@@ -38,10 +38,15 @@ class VectorSpaceBasis(object):
         return self._nullspace
 
     def orthogonalize(self, b):
-        """Orthogonalize ``b`` with respect to this :class:`.VectorSpaceBasis`.
+        """Return a copy of ``b`` orthogonalized with respect to this :class:`.VectorSpaceBasis`.
 
         :arg b: a :class:`.Function`"""
-        raise NotImplementedError
+        ret = Function(b)
+        with b.dat.vec_ro as bv:
+            for v, iv in zip(self._vecs, self._petsc_vecs):
+                dot = iv.dot(bv)
+                ret += -dot * v
+        return ret
 
     def is_orthonormal(self):
         """Is this vector space basis orthonormal?"""