Absolute homogeneity of a norm
= Absolute homogeneity of a norm
{title2=$\|av\|=|a|\,\|v\|$}
Absolute homogeneity is the <norm> axiom $\|av\|=|a|\|v\|$ for every <scalar> $a$ and <vector> $v$. It distinguishes a <norm> from a merely homogeneous expression of a different degree; for example the fourth root in the <box norm> converts a degree-four expression into a degree-one <norm>.