I am reading a lectre notes of Power method. You can find the notes here
For a symmetric matrices $M$, pick a randomm unit vector $x$. If we write $x$ as $\sum_ia_ie_i$, where $e_i$ is eigenvectors and $\lambda_i$'s are numbered in decreasing order by absolute value. Then $t$ iteration produce $M^tx=\sum_ia_i\lambda^t_ie_i$. Since $x$ is a unit vector, $\sum_i a^2_i=1$. Suppose there is a gap of $\gamma$ between the top two eigenvalues: $\lambda_1-\lambda_2=\gamma$. Since $|\gamma_i|\leq|a_1|-\gamma$ for $i\geq2$, we have: $\sum_{i\geq2}|a_i^t|\leq n(a_1-\gamma)^t=n|a_1|^t(1-\gamma/|a_1|)^t$
I don't understand how can we derive the condition $|\gamma_i|\leq|a_1|-\gamma$