Having established that the transformations in question are unitary,
and thus physically realizable, it is left to establish that
iterations of Grover's algorithm increase the amplitude of the marked
state
*C*(*S*_{m}) = 1 enough that the probability of measuring state
*S*_{m} is at least 1/2 in
*O*() operations.

We start by examining the effect of the inversion about average
operator *A*.