For a full rank matrix A, its null space basis can be computed from its LU factorization. In fact exactly this is implemented in Eigen in the class
FullPivLU< MatrixType > Class Template Reference ---- look at http://eigen.tuxfamily.org/dox/classEig ... 13b6e7200a for
const internal::kernel_retval<FullPivLU> kernel() const

However, it seems this is not possible to do for a sparse matrix in Eigen. There is actually no way of computing a null space matrix Z, such that AZ=0 for a (large) sparse matrix A. Since Eigen is such a great library, it would be a shame not to implement such a useful computational tool (i.e. the ability to compute a null space basis from sparse QR or sparse LU) for sparse matrices too.

Is there a plan to make this possible in Eigen (see SuiteSparse and LUSOL implementations)?

Thanks in advance.

Sure, this would be a very welcome addition. Patch welcome