euclidean length, vector length

definition

• square-root of the sum of squares of the components of x
• extension to multidimensional case of pythagoras ($R^2$)
• $euclideanlengthx=\sqrt{x_1^2+x_2^2+\cdot \cdot \cdot \cdot +x_n^2}.$
• also called $I_{2}norm$
• $\Vert x{\Vert }_2^2=x^{\top }x$