I am computing the characteristic polynomial of a matrix over a number field, using the minimal polynomial of it. Is there a fast way to verify the characteristic polynomial of a big matrix ?



How to verify the characteristic polynomial?
You can pick $n+1$ numbers and evaluate the determinant $det(A-tE)$ at these values. This gives you a garantee, but if you just want a rough check, you can pick smaller amount of (random) numbers and evaluate the determinants modulo some prime numbers (which is usually faster).


