Question: Problem number 5 5. Let P be a nonzero projector and || Pll2 = 1. Prove that a) P is an orthogonal projector. b) I

Problem number 5

5. Let P be a nonzero projector and || Pll2 = 1. Prove that a) P is an orthogonal projector. b) I - 2P is unitary. 6. Assume A is a real symmetric matrix and has an LU factorization. Prove that A can be written as A = LDL , where D is diagonal and L is lower-triangular

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