I am given the following definition of the power method:
The Power method is the classical method to compute the largest few eigenvalues of a matrix. The method is motivated by the property that if we multiply a vector by a matrix, the contribution of the eigenvector corresponding to the largest eigenvalue (in absolute value sense) increased more than the contribution of the other eigenvectors. If the vector is multiplied a large number of times by the matrix, the contribution of this eigenvector will dominate, so the resulting iteration vector will approximate this eigenvector. So we arrive at the following algorithm.
The Power method:
$q_0\in\mathbb{C} \text{ is given }\\\text{for $k=1,2,3,\ldots$}\\\space z_k = Aq_{k-1}\\\space q_k = z_k/\|z_k\|_2\\\space\lambda^{(k)} = \bar{q}_{k-1}^Tz_k$
Question: What is meant by "the contribution of the eigenvector corresponding to the largest eigenvalue (in absolute value sense) increased more that the contribution of the other eigenvectors"? I've tried to understand this intuitive explanation of the power method but somehow it doesn't make sense to me.
Thanks in advance!