Confusing terminology in singular-poisson demo

[Nikolaus Rath]

http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/singular-poisson/python/documentation.html says:

--snip--
AU=b

where U gives the coefficient for the basis functions expressing u.

Since we have pure Neumann boundary conditions, the matrix A is singular. There exists a vector e such that
Ae=0.

span {e} is the null space of A, and by removing the components of b that lie in the null space we make the system solvable.
--snip--

The last part does not make sense to me. Let A be a linear operator from V to W. Then the null space is a subspace of V, but b is defined in W. Therefore, it doesn't make sense to talk about components of b that lie in the null space.

I think a better formulation is

--snip--
AU=b

where U gives the coefficient for the basis functions expressing u.

Since we have pure Neumann boundary conditions, the matrix A is singular. There exists a vector e such that
Ae=0. We make the system solvable by removing the components of b that do not lie in the column space of A, which are also the components that lie in the null space of transpose(A).
--snip--

[Johannes Ring (johannr)]

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