To calculate the eigenvalues of H you have to chose, either to use your implementation where H is a handle to a function returning an ordinary matrix if you feed it an input argument. This for example works fine:
eig(H(3))
Since:
H(3)
returns a matrix:
ans =
1.5000 0 0 0
0 -1.5000 3.0000 0
0 3.0000 -1.5000 0
0 0 0 1.5000
That has some eigenvalues. Or you could go with symbolic calculations:
syms x;
eig([x/2,0,0,0;0,-x/2,x,0;0,x,-x/2,0;0,0,0,x/2])
