1. The problem statement, all variables and given/known data Find the oblique projector P so where range(P) = range(U) and range(I-P) = range(W) 2. Relevant equations P^2-P = 0 range(I-P) = null(P) 3. The attempt at a solution It seems that U and W are complementary subspaces. According to: http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.4500v4.pdf U*(V*U)t*V where t is the Moore-Penrose inverse. The task is to be done in Matlab. My problem is that V and U cannot be multiplied due to their sizes. The sizes are for example (5,3) and (5,8) with the rows in common. I tried adding on the identity to fill up space in U and also tried to add null space but this did not work. I always seem to end up with a projector P so that: P^2-P = 0 PA = A but PB != 0 and (I-P)B != B Any ideas?