Let V {\displaystyle {}V} be a K {\displaystyle {}{\mathbb {K} }} -vector space, endowed with an inner product ⟨ − , − ⟩ {\displaystyle {}\left\langle -,-\right\rangle } , and let U ⊆ V {\displaystyle {}U\subseteq V} denote a linear subspace. Show that the restriction of the inner product to U {\displaystyle {}U} is again an inner product.
