# Definition
$$L: V \to \mathbb{C}^n \; \text{bijective}$$
$$L (ax + by) = a \times L(x) + b \times L(y), \; \forall x, \, y \in V, \, a; \, b \in \mathbb{C}$$
$$\| \, L(x) \, \|  = \| \, x \, \|, \; (L(x) | L(y)) = (x | y)$$