Linear Algebra. Points matching with SVD in 3D space

We need to find best rotation & translation params between two sets of points in 3D space. This type of transformation called Euclidean as it preserves sizes. There are many ways of getting things done almost in any case, but currently we will use SVD for this. You ask why? -- Because matrix is basically a transformation and with SVD can be decomposed on Rotation(U), Scaling(Σ), Rotation(V) (in special case when A is mxm matrix, but this gives us a clue. To get rotation first we need to find out center of it.