Linear mapping/Angle-preserving/Definition

Angle-preserving mapping

A linear mapping

$\phi :V⟶W$

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

$\mathrm{\angle }(\phi (u),\phi (v))=\mathrm{\angle }(u,v)$

holds.