Linear Map

Definition

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