Distance of infinity norm

  • #1
Alright, so if I want to find the distance of the ∞-norm between two vectors in lR^3, then would I take the max of the vectors first and then subtract, or should I subtract the vectors and then take the max? I think that the vectors are subtracted, and then the norm is taken, but I just want to make sure.
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  • #2
You have it correct: find the difference, then apply the norm. This is the definition of a normed distance (i.e., that is how you calculate the distance in any metric space where distance is defined by some norm on the space).
  • #3
In fact, in any norm, the distance between two vectors u and v is given by ||u- v||.

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