Absolute homogeneity of a norm ($\Vert av\Vert =|a|\Vert v\Vert$)

Absolute homogeneity is the norm axiom $\Vert av\Vert =|a|\Vert v\Vert$ 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.