Unit-Norm Vectors under Different p-Norms

This Demonstration shows how unit-norm vectors look under different -norms, which are standard norms for finite-dimensional spaces.
In mathematics, a norm is a function that assigns a length (or size) to a vector. The vector is an object in a vector space, and can thus be a function, matrix, sequence, and so on. A -norm is a norm on a finite-dimensional space of dimension defined as
.
This Demonstration shows sets of unit-norm vectors for different -norms.
The norm for is called the Manhattan or taxicab norm because represents the driving distance from the origin to following a rectangular street grid
The norm for is the usual Euclidean square norm obtained using the Pythagorean theorem
The norm for is simply the maximum over and ,
Vectors ending on the red lines are of unit norm in the corresponding -norm.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

References
[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014. www.fourierandwavelets.org.
[2] Wikipedia. "Norm." (Jun 12, 2012) en.wikipedia.org/wiki/Norm_%28 mathematics %29.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.