Google Classroom
GeoGebraGeoGebra Classroom

p-norm ball

p norm un a vector space

A norm in a vector space is a function that asign a positive real number to each vector, is positive-scalar multiplicative and satisfies the triangular inequality. 1. for every and 2. for every and every scalar 3. for every pair Each norm naturaly define a distance that makes the vector space a metric space. The distnace is defined by In the plane R2 we can obtain a very well studied group of norms, named the p-norms. Consider , and define for We define the p-norm ball as the set of all vectors in such that de p-distance to the origin is less than 1. In the following animation we can see the plot of the border of the p-ball for some values of p moving from 1 to 4.