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Norm inequality, find coefficients

  1. Sep 5, 2016 #1
    • Member warned that homework posts must include an effort
    1. The problem statement, all variables and given/known data
    Find coefficients a,b>0 such that a||x||≤||x||≤b||x||.


    2. Relevant equations


    3. The attempt at a solution
    No idea how to get started. Help will be appreciated.
     
    Last edited by a moderator: Sep 5, 2016
  2. jcsd
  3. Sep 5, 2016 #2

    Math_QED

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    You must have tried something? You must have thought something? Share it with us because you are required to show some effort.
     
  4. Sep 5, 2016 #3
    I have no idea how to find the coefficients...and I am not expecting you to do my homework.

    it has something to do with equivalence of norms?
     
    Last edited: Sep 5, 2016
  5. Sep 5, 2016 #4

    pasmith

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    How is [itex]\|x\|[/itex] defined?
    How is [itex]\|x\|_{\infty}[/itex] defined?
    What is the dimension of the space on which these norms are defined?
     
  6. Sep 5, 2016 #5

    Ray Vickson

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    Yes, that is exactly what the problem is about---showing how to prove norm equivalence.
     
  7. Sep 5, 2016 #6

    micromass

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    What space is ##x## a member of? How are the norms defined?
     
  8. Sep 5, 2016 #7

    Mark44

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    @lep11, definitions of these two norms would have been useful in the (empty) Relevant equations section.
     
  9. Sep 6, 2016 #8
    ##\|x\|:=(\sum_{i=1}^{n} x_i^2)^½##
    [itex]\|x\|_{\infty}[/itex]:=max{|x1|,...,|xn|}

    x∈Rn, so dimension of the space is n.
     
  10. Sep 6, 2016 #9

    Ray Vickson

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    Why don't you look first at the case of ##n=2##, where you can easily draw pictures and make ##(x_1,x_2)##-diagrams to help you focus your thinking?
     
  11. Sep 6, 2016 #10

    Mark44

    Staff: Mentor

    At 9 posts into this thread, the OP still has not shown an attempt -- thread closed.

    @lep11, you may start another thread on this question, but you MUST show some effort or there will be consequences.
     
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