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## Homework Statement

Find the oblique projector P so where range(P) = range(U) and range(I-P) = range(W)

## Homework Equations

P^2-P = 0

range(I-P) = null(P)

## 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?