Zig Zag Product's

Question

Hi I read this paper about the Zig Zag Product's (page 73-74)

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

Notice how $f^\perp$ and $f^\parallel$ are orthogonal to each other. Then apply the Pythagorean theorem for Hilbert spaces.