# Finding a matrix representation of a Hamiltonian.

## Homework Statement

The Hamiltonian H for a certain physical quantum mechanical system has three eigenvectors {|v1>, |v2>, |v3>} satisfying:
H|vj> = (2-j)a|vj>

Write down the matrix representing H in the representation {|v1>, |v2>, |v3>} .

## The Attempt at a Solution

I though the Hamiltonian would just be the eigenstates along the diagonal, however this seems too simple.
a 0 0
0 0 0
0 0 -a​