Oblique projector

  • Thread starter kalleC
  • Start date
  • #1
11
0

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?
 

Answers and Replies

  • #2
11
0
p = [U 0] [U V]^-1

According to "Generalized inverses: theory and applications" by AvAdi Ben-Israel, Thomas Nall Eden Greville

0 is nullspace

And sure as hell it works =D
 

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