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Wednesday, August 28, 2013

unit circle under different norms

Using the p-norm defined as
||x||p=(ni=1|xi|p)1/p
for p>0, we can look at what a unit circle is for each norm. Note that for 0<p<1 the formula above is not actually a norm as it violates the triangle inequality required to be a norm. Regardless, let's look at what a unit circle looks like in 2D for a few of the norms:
Isn't it cool how the corners of the unit circle get pushed out as the order of the norm increases! 


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