Linear mapping/Angle-preserving/Definition

A linear mapping

${\displaystyle \varphi \colon V\longrightarrow W}$

between Euclidean vector spaces ${\displaystyle {}V}$ and ${\displaystyle {}W}$ is called angle-preserving, if for any two vectors ${\displaystyle {}u,v\in V}$ (different from ${\displaystyle {}0}$) the relation

${\displaystyle {}\angle (\varphi (u),\varphi (v))=\angle (u,v)\,}$

holds.