Definition

The 2-Norm, denoted as $\|\cdot\|_{2}$, for any arbitrary $v\in V$ is defined as follows: $$\begin{align*} \mathbb{F}^{n}&: \ \|v\|_{2}=\sqrt{|v_{1}|^{2}+\cdots+|v_{n}|^{2}}\\ \mathbb{F}^{\infty}&:\|(v_{i})_{i\in\mathbb{N}}\|_{2}=\left(\sum\limits_{i=1}^{\infty}|v_{i}|^{2}\right)^{\frac{1}{2}}\\ C^{0}([a,b];\mathbb{F})&:\|f\|_{2}=\left(\int_{a}^{b}|f(x)|^{2}dx\right)^{\frac{1}{2}} \end{align*}$$