## How To Measure Size Of Vector

23 May 2017

Hello everybody,

today I want to share with everybody information about function that is known as norm. Here it is:

# ||x|| _{p} = ( Σ(|x|_{i})^{p})^{ p -1}

For p ∈ R, p ≥ 1

Also it is named as L^{p} norm. On intuition level it measures distance from some beginning point to locatio of x.

L^{2} norm is often named Euclidian norm. Also due to heavy usage L^{2} is presented just as ||x|| with skipped 2. It means that if you see ||x|| it was intended to show you ||x||_{2}.

Sometime you can find L^{∞} norm. It is nothing more then maximum value of vector.

||x||

_{∞}= max_{i}|x_{i}|.