Standard Inner Product Function

Standard Inner Product for Complex Numbers

Define $f_a:{\mathbb{C}}^n\to \mathbb{C}$ where $f_{\alpha }=⟨v|a⟩,\forall v\in V$

Standard Inner Product for Real Numbers

Define $f_a:{\mathbb{R}}^n\to \mathbb{R}$ where $f_{\alpha }=⟨v|a⟩,\forall v\in V$