vector distance, euclidean distance

definition

• $d(x,y)=\Vert x-y{\Vert }_2$, with $x,y\in {\mathbb{R}}^n$
• $\Vert x+y{\Vert }_2^2=(x+y{)}^T(x+y)=\Vert x{\Vert }_2^2+\Vert y{\Vert }_2^2+2x^{T}y$
• triangle inequality: $d(x+y)\le d(x)+d(y)$