Linear Algebra Done Right · Problem 6A.20

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products-and-norms

Problem

Prove that if

u, v \in V

, then

\big|\|u\| - \|v\|\big| \leq \|u - v\|

. The inequality above is called the reverse triangle inequality. For the reverse triangle inequality when

V = \mathbf{C}

, see Exercise 2 in Chapter 4.