Isometry/Invariant linear subspace/Exercise

Let $V$ be a $𝕂$-vector space, endowed with an inner product. Let

$\phi :V⟶V$

be an isometry, and let $U\subseteq V$ be a $\phi$-invariant linear subspace. Show that

$\phi {|}_U:U⟶U$

is also an isometry.

Create a solution