Find the smallest eigenvalue exactly

I would like to find the smallest (in absolute value) nonzero eigenvalue of the matrix exactly. I can do this using floating point arithmetic using numpy, but

• Is there any way to get an exact answer?
• Do you need to use sympy for this or is there another way?

Matrices will be small (say, less than 20 by 20) with integer values. When I say the exact answers, I mean, for example, the answer to John Habert’s question .