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## Homework Statement

Let A be a Hermitian matrix and consider the matrix U = exp[-iA] defined by thr Taylor expansion of the exponential.

a) Show that the eigenvectors of A are eigenvectors of U. If the eigenvalues of A are a subscript(i) for i=1,...N, show that the eigenvalues of U are exp[-i*a subscript(i)].

b) Show that U is unitary.

This example is important in quantum mechanics when A=Ht/h, where H is the Hamiltonian operator, t is time, and h is Plank's constant. Then U evolves the wavefunction over a time t.

## Homework Equations

I have uploaded what I have come up with so far, but not sure where to go with it

## The Attempt at a Solution

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See uploaded file