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Question 1:
Consider the matrix A given by
(a) calculate eigenvalues λ1 and λ2 and obtain the corresponding normalized eigenvectors v^1 and v^2 for A. It should be apparent at the outset, from the structure of A, that the eigenvectors may realized as an orthonormal set. Why?
(b) Show by direct calculation that A may be written as
A = U†DU
where U is a unitary matrix and D is a matrix with nonzero entries only on the main diagonal.
Question 2:
Use the results of 1) to show that
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