  The control of quantum walk is made particularly transparent when the initial
state is expressed in terms of the eigenstates of the coin operator. We show
that the group-velocity density acquires a much simpler form when expressed in
this basis. This allows us to obtain a much deeper understanding of the role of
the initial coin state on the dynamics of quantum walks and control it. We find
that the eigenvectors of the coin result in an extremal regime of a quantum
walk. The approach is illustrated on two examples of quantum walks on a line.
