Real finite-dimensional vector space/Oriented/Isomorphism/Orientation-preserving/Definition

Orientation-preserving linear mapping

Let ${}V$ and ${}W$ be finite-dimensional oriented real vector spaces. A bijective linear mapping

$\varphi \colon V\longrightarrow W$

is called orientation-preserving, if for every basis ${}v_{1},\ldots ,v_{n}$ representing the orientation on ${}V$, the image vectors ${}\varphi (v_{1}),\ldots ,\varphi (v_{n})$ represent the orientation on ${}W$.