- #1
Mattbringssoda
- 16
- 1
Homework Statement
Let q ∈ C^m have 2-norm of q =1.
Then P = qq∗ is a projection matrix.
(a) The matrix P has a singular value decomposition with U = [q|Q⊥] for some appropriate matrix Q⊥.
What are the singular values of P?
(b) Find an SVD of the projection matrix I − P = I − qq∗ . In particular, what are the singular values? Hint: Write I = UU∗ where U is as above and use the SVD of qq∗ .
Homework Equations
The Attempt at a Solution
[/B]
I'm afraid I'm at a loss for what I should aim for as far as an answer. Here's what I've been working on...
a)
with the above matrix coming from the equation of U in the instructions.
So, I can answer that the singular values are the diagonals of Σ, which I now have an equation for...however it feels like I'm supposed to take this a step further...would anyone have any insight??
b)
And again I can't help but feel this is too general or that I'm missing something.
Thanks for any help!