Let \( V \) be an inner product space . The canonical map from \( V \) into its dual \( V^* \) is the map
\[ \Phi : v \mapsto \langle \cdot, v \rangle. \]It is injective , antilinear, and isometric .
Remarks
- If \(V\) is a Hilbert space , \(\Phi\) is a linear isomorphism (see (0x68e72ea1) ).