Question: Let (a) Verify that T is hermitian. (b) Find its eigenvalues (note that they are real). (c) Find and normalize the eigenvectors (note that they

Let

1-i = ( +1 0'). +i T = (

(a) Verify that T is hermitian.
(b) Find its eigenvalues (note that they are real).
(c) Find and normalize the eigenvectors (note that they are orthogonal).
(d) Construct the unitary diagonalizing matrix S, and check explicitly that it diagonalizes T.
(e) Check that and Tr(T) are the same for T as they are for its diagonalized form.

1-i = ( +1 0'). +i T = (

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