9814

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, Signal Processing: Foundations, Cambridge: Cambridge University Press, forthcoming. 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.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+