Vector pNorms
This module graphically illustrates vector
pnorms in two dimensions. For any integer
p > 0, the pnorm of an
nvector x is defined by
Important special cases include

Manhattan norm, the distance between two points measured in
“city blocks”, given by p = 1

Euclidean norm, the usual notion of distance in Euclidean
space, given by p = 2

Infinity or max norm, given by the limit as
p → ∞,
For any given norm, the unit circle is the set of all points
having norm 1, although it is a circle in the conventional sense only
for p = 2. As this module illustrates, the norm of
any vector is given by the scalar factor by which the unit circle in
that norm must be expanded or shrunk to encompass the vector
exactly.
The user first selects a vector by clicking on the graph. The
vector selected is shown by an arrow in the graph and also by its
numerical coordinates in the right panel. The user then selects a
value for p from the menu provided. To determine the
pnorm of the vector, the user drags the unit
circle for the chosen pnorm until it exactly
encompasses the chosen vector. The resulting numerical value of the
norm is shown in the right panel. Other norms can be tried for the
same vector by selecting a new value for p from the menu, or a
new vector can be selected by clicking Reset.
Reference: Michael T. Heath,
Scientific Computing,
An Introductory Survey, 2nd edition, McGrawHill, New York,
2002. See Section 2.3.1 and Figure 2.2.
Developers: Sukolsak Sakshuwong and Michael Heath