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Homework Help: Euclidean metric (L2 norm) versus taxicab metric(L1 norm)

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data

    I was just wondering how I would go about proving that the euclidean metric is always smaller than or equal to the taxicab metric for a given vector x in R^n. The result seems obvious but I am not sure how I would show this.



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 26, 2010 #2

    D H

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    Show that (||x||1)2 - (||x||2)2 can never be negative.
     
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