how to properly substitute in a matrix?

edit

Try this:

sage: solutions=solve(list(f.diff()),[x,y],solution_dict=True)
sage: solutions
[{y: 0, x: -I}, {y: 0, x: I}, {y: -1/2, x: 0}]
sage: H.subs(solutions[2])
[(x, y) |--> -1  (x, y) |--> 0]
[ (x, y) |--> 0  (x, y) |--> 2]

Or this:

sage: H(x,y).subs(solutions[2])
[-1  0]
[ 0  2]

I'm not sure exactly what output you are looking for.

The documentation for solve has some more information about this keyword.