1. The problem statement, all variables and given/known data 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∗ . 2. Relevant equations 3. The attempt at a solution 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!!