Euclidean vector space

Euclidean vector space is a finite-dimensional real inner product space.

Euclidean norm is induced on a Euclidean vector space. Specifically, the norm operation \(||\cdot||:\mathbb{V} \to \mathbb{R}_{\geq 0}\) can be defined using the (real) inner product operation as

\[||\cdot||=\sqrt{\langle \cdot, \cdot \rangle}\]