Question: Could you help giving me explanations on the problem below ? Thank you. Linear Algebra . [i - Let W be an inner product space

Could you help giving me explanations on the problem below ? Thank you. Linear Algebra

. [i - Let W be an inner product space and suppose T is a linear operator on W with adjoint T*. (a) Prove that if T*T = 144 - IW, then ||T(:r)|| = 12||33|| for all :1: E W. (b) Suppose W is not the zero vector space. Is it possible for T*T = 42' - IW? Explain your

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