How do I calculate the distance of the ∞-norm between two vectors in lR^3?

[Mindscrape]

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.

 

[D H]

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).

 

[HallsofIvy]

In fact, in any norm, the distance between two vectors u and v is given by ||u- v||.