Question: 8. (a) Let P be a self-adjoint projection on a complex inner product space. Show that H := I - 2P is an isometry. (b)

8. (a) Let P be a self-adjoint projection on a complex inner product space. Show that H := I - 2P is an isometry. (b) Does left multiplication by the complex (3 x 3)-matrix C := O define a normal operator on the standard complex inner product space C3

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