Euclidean vector spaces/Orthogonal to orthogonal/Injective/Angle-preserving/Exercise

Let ${}V$ and ${}W$ be Euclidean vector spaces, and let

$\varphi \colon V\longrightarrow W$

denote an injective linear mapping, fulfilling the property that orthogonal vectors are mapped to orthogonal vectors. Show that ${}\varphi$ is angle-preserving.

Create a solution