A <norm> on a real or complex <vector space> $V$ is a function $\|\cdot\|:V\to[0,\infty)$ with $\|v\|=0$ exactly when $v=0$, $\|\lambda v\|=|\lambda|\|v\|$, and the <triangle inequality> $\|v+w\|\le\|v\|+\|w\|$. These are positivity, absolute homogeneity and the <triangle inequality>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / ib / Paper 2 / 12G / a / Solution

 Solution (source code)