Question: need help with these, for better understanding :( Fix u, x e V with u 0. Define Te C(V) by Tv = (v, u)x for

need help with these, for better understanding :(

Fix u, x e V with u 0. Define Te C(V) by Tv = (v, u)x for every ve V. Prove that T * Tv = (v, u)u for every ve V. Give an example of T e C(C2) such that 0 is the only eigenvalue of T and the singular values of T are 5, 0

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