Zig Zag Product's Equation

Question

Hi I read this paper about the Zig Zag Product's (page 73 below)

http://www.cs.huji.ac.il/~nati/PAPERS/expander_survey.pdf

and I encounter this equation.

but I did not understand why this is true.

Answer 1

Page 73: $f^{\parallel} = \frac{1}{m} \cdot \sum_{j\in[m]} f(x,j)$ by definition.

$||g||^2 = m^2 \cdot ||f^{\parallel}||^2 = ||f||^2$