I use the Direct Linear Transform (DTL) to estimate a homography from a given set of point correspondences $(x_i,x_i')$, such that $$x_i' = \mathbf{H}x_i$$ Therefore, I set up the measurement matrix $\mathbf{A}$ as usual and solve $$\mathbf{Ah} = \mathbf{0},\quad \mathbf{h}=[H_{1,1}, H_{1,2}, \dots, H_{3,3}]$$ using the SVD of $\mathbf{A} = \mathbf{U\Sigma V}^T$. The least-norm solution is then given by the right singular vector that corresponds to the smallest singular value $\sigma_9$ and the norm of the residual is given by $\lVert\mathbf{Ah}\rVert_2^2 = \sigma_9$.
However, usually the coordinates are normalized such that their centroid is at the origin and their average distance to the origin is $\sqrt{2}$ using a transform matrices $\mathbf{T}$ and $\mathbf{T}'$, such that $\hat{\mathbf{x}} = \mathbf{Tx}$ and $\hat{\mathbf{x}}' = \mathbf{T}'\mathbf{x}'$ yielding $\hat{\mathbf{H}}$ as and intermediate result. Then $\mathbf{H} = \mathbf{T}'^{-1}\hat{\mathbf{H}}\mathbf{T}$.
How can I recover the norm of the residual in that case?