Label the following statements as true or false. Assume that the underlying inner product spaces are finite-dimensional. (a) Every self-adjoint operator is normal. (b) Operators and their adjoints have the same eigenvectors. (c) If T is an operator on an inner product space V, then T is normal if and only if [T]β is normal, where β is any ordered basis for V. (d) A real or complex matrix A is normal if and only if LA is normal. (e) The eigenvalues of a self-adjoint operator must all be real.(f) The identity and zero operators are self-adjoint. (g) Every normal operator is diagonalizable. (h) Every self-adjoint operator is diagonalizable

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A: Since you have posted a question with multiple subparts, we will solve the first two subparts…

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A: Hey since there are multiple subparts the first four is answered. If any other subpart is required…

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A: I just used definition of eigen vector

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A: Note : according to our gauidlines i can solve only first 3 subpart, please reroute the remaining…

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A: i uave used the definition of diagonalisation

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A: (a) This can be proved as follows:

Q: Please see image

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