I don't know if you're into physics, but if you are, quantum mechanics is a fantastic follow-up to linear algebra. Prerequisites for quantum mechanics (in my opinion) are:
Freshman and Sophomore-level physics.
Junior-level classical mechanics (although I survived without having had that first - it is a little better if you do it first).
Calculus 1, 2, and 3.
That'd be my recommendation. If you're not into applications so much, you might go with Advanced Calculus, Real Analysis, Complex Analysis (a particularly beautiful subject), or even Abstract Algebra.