Corollary 1.2: Let the state vector be as follows:

- For the marked state
*S*_{m}such that*C*(*S*_{m}) = 1, the amplitude is*k* - For all other (
*N*- 1) states the amplitude is*l*

Proof: This follows directly from the fact that *A* is unitary, and
that unitary transformations preserve normalization of the state
vector. That means precisely that the sum of the absolute squares of
the components is the same before and after the operation. Since we
never deal with any complex amplitudes in the processing of Grover's
algorithm, corollary 1.2 follows directly. [Grover96]