Question from Boyd's Optimization Book

[newphysist]

Hi,

I am reading Convex Optimization from Stephen Boyd's book on my own and I am stuck at math he mentions on Pg. 157 of his book which can be found here.

How does he write the following:

sup{u^TP$^{T}_{i}$x | ||u||₂ ≤ 1} = ||P$^{T}_{i}$x||₂

Thanks guys

 

[jasonRF]

I didn't attempt to find this in the book, but to me this looks like a direct result of the Cauchy-Schwarz inequality.

http://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

jason