"Measuring" vectors is done by specifying a norm, a datum which measures lengths of vectors, or by an inner product, which measures angles between vectors. Norms and inner products are denoted | v | and ⟨ ⟨ v , w ⟩ ⟩ , respectively. The datum of an inner product entails that lengths of vectors can be defined too, by defining the associated norm | v | := ⟨ ⟨ v , v ⟩ ⟩ . Vector spaces endowed with such data are known as normed vector spaces and inner product spaces, respectively.