, Peggy sends c A as the characteristic polynomial

, Peggy and Victor enter a determinant certificate for rI ? A

, Once convinced, Victor checks that det(rI ? A) ? == c A (r)

, For a random r ? S, in the determinant sub-certificate, rI ? A will be nonsingular if c A (r) = 0, hence with probability ? 1 ? n/|S|. Then det(rI ? A) is certified using the certificate of Figure 5. Best known algorithms for computing the characteristic polynomial, using either quadratic space and fast matrix multiplication or linear space

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