/// <summary>
/// Return N s.t.\ M' * N = 0.
/// </summary>
/// <returns></returns>
public MatrixFixed LeftNullspace()
{
int k = Rank();
if (k == n_)
{
Debug.WriteLine("VNL::SVD<T>::LeftNullspace() -- Matrix is full rank." + Convert.ToString(last_tol_));
}
return(U_.Extract(U_.Rows, n_ - k, 0, k));
}
/// <summary>
/// Return N s.t.\ M * N = 0.
/// </summary>
/// <param name="required_nullspace_dimension"></param>
/// <returns></returns>
public MatrixFixed Nullspace(int required_nullspace_dimension)
{
return(V_.Extract(V_.Rows, required_nullspace_dimension, 0, n_ - required_nullspace_dimension));
}
