EDB — 0ZY

Exercises

1. [0ZY] Note that if \(v,w∈ X\) are linearly dependent and have the same direction (i.e. you can write \(v=𝜆 w\) or \(w=𝜆 v\), for \(𝜆≥ 0\)), then you have

   \[ \| v+w\| = \| v\| +\| w\| \quad . \]

   In particular, a norm is not a strictly convex function, because

   \[ \| \frac{v} 2+\frac{v} 2\| = \frac 1 2 \| v\| +\frac 1 2\| v\| \quad . \]