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Math Help - L1-, L2-, Linfty-Norm Proofs - Please Help!

  1. #1
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    Question L1-, L2-, Linfty-Norm Proofs - Please Help!

    Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers.

    ||x||2 is defined here: L2-Norm -- from Wolfram MathWorld
    ||x||1 is defined here: L1-Norm -- from Wolfram MathWorld
    ||x||infinity is defined here: L1-Norm -- from Wolfram MathWorld

    Sorry about posting links, but I have no idea how to get all the symbols (like the summation symbol) to show up on the forums.

    Anyway, thanks in advance for your help!
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  2. #2
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    Quote Originally Posted by theamazingjenny View Post
    Show that ||x||1 < or = n||x||infinity and ||x||2 < or = sqrt(n)*||x||infinity for x exists in the set of all real numbers.

    ||x||2 is defined here: L2-Norm -- from Wolfram MathWorld
    ||x||1 is defined here: L1-Norm -- from Wolfram MathWorld
    ||x||infinity is defined here: L1-Norm -- from Wolfram MathWorld

    Sorry about posting links, but I have no idea how to get all the symbols (like the summation symbol) to show up on the forums.

    Anyway, thanks in advance for your help!
    What is x and what is n. By the look of this you intend x in R^n.

    If so the first of these is trivial:

    ||x||_1 = sum_{i=1 to n} |x_i| < n max_{i=1 to n} |x_i| = n ||x||_{infty}

    and the other is no more difficult

    RonL
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