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 ?
closed as off-topic by YCor, Greg Martin, abx, Neil Hoffman, Per Alexandersson Nov 27 '18 at 21:11
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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).