Euclidean vector spaces/Angle-preserving/Functorial properties/Exercise

Let ${}U,V$ and ${}W$ be Euclidean vector spaces. Show that the following statements hold.

a) The identity

$\operatorname {Id} _{V}\colon V\longrightarrow V$

is angle-preserving.

b) The composition of angle-preserving mappings

$\varphi \colon U\longrightarrow V$

and

$\psi \colon V\longrightarrow W$

is again angle-preserving.

c) For a bijective angle-preserving mapping

$\varphi \colon U\longrightarrow V,$

the inverse mapping is also angle-preserving.

Create a solution