I am curious what is the precise math reasoning behind this:
$ \sup \{ a_i^T u | \lVert u\rVert_2 \leq r \} = r \lVert a_i \rVert_2$
It is on page 148, last line, of Boyd's Convex Optimization text.
I realize the statement is saying: the supremum of a dot b is equal to the length of a times the maximum length of b, but I was wondering if there was any other way to explain the reasoning.
Thank you all.