Length of a Vector

The length (or magnitude) or a vector is represented using the “double absolute value” sign, and is defined as:

$$||\vec{u}||=\sqrt{\vec{u}\cdot \vec{u}}=\sqrt{u_1^2+u_2^2+\cdots +u_n^2}$$

where:

• $\vec{u}=\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ u_n\end{array}\right]$
• $\vec{u}\cdot \vec{u}$ is the dot product of $\vec{u}$ with itself.