EOF real vector analysis of current field

I have a little doubt about the procedure to compute the real-vector EOF analysis for velocity fields described in Kaihatu et al. 1998. Considering that I have N grid points with velocities for T time steps, I understand that I have to apply the svd decomposition to a 2NxT matrix where the first N rows correspond to the U points and the N+1 to 2N rows correspond to V. My doubt is: once the decomposition is performed (for example for the first 10 EOF modes) I obtain a 2Nx10 EOF matrix. Here I understand that again the first N rows correspond to the U component for that mode and from N+1 to 2N to V. Is it that correct? I'd really appreciate any help.

Thanks