DynCont#3: SVD, MIT 18.065 Strang you tube lecture video 6

1.  We are looking for a bunch of orthogonal vectors u, which when multiplied by A, give another set of orthogonal vectors v, scaled by sigma
2. Curse of Dimensionality =   A matrix is basically scaling and rotation. For a 2x2 matrix, there are 4 terms . it has 2 scaling values and 2 rotations. The rotations increase the time taken. not the scaling. For 3x3 matrix, there are 9 independent terms with 6 rotations and 3 scaling terms. Similarly, 4x4 matrix has 4 scaling terms and 12 rotations.
3. Rank= If A has rank r, there are r orthogonal vectors , which when multiplied by A give another r orthogonal vectors.
4. If U vectors are orthogonal in AU=sigma V, it can be proven that V vectors are orthogonal by simply substituting VV' = (AU/Sigma1)* (AU/Sigma1)'