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.

[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Signal Processing: Foundations, Cambridge: Cambridge University Press, forthcoming. www.fourierandwavelets.org.