Euclidean Length

Description:

• $|x{|}_2\doteq \sqrt{{\sum }_{k=1}^n{x}_k^2}$
  • For every $x\in {\mathbb{R}}^n:||x|{|}_2^2=x^{T}x$
  • $||x|{|}_2=1$ forms a circle
• The square-root of the sum of square of components of $x$
• Euclidean Length of $x=\sqrt{x_1^2+x_2^2+...+x_n^2}$

Root Mean Square

Variance using $l_2$ norms:

• Variance: $\text{var}(x):=\frac{1}{n}||\tilde{x}|{|}_2^2$

Correlation coefficient using $l_2$ norms:

• Vector’s Correlation