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Show Matrix 2-Norm Greater than Matrix Inf-Norm

  1. Sep 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Show [tex]\sup _{x \neq 0}\|Ax\|_\infty/\|x\|_\infty\leq\|Ax\|_2/\|x\|_\infty[/tex]

    2. Relevant equations
    See above.


    3. The attempt at a solution
    I'm not looking for a full solution, just a push in the right direction. I've tried breaking out the numerators such that [tex]\|Ax\|\leq\|A\|\|x\|[/tex] on both sides and multiplying through, as well as trying to use [tex]\|x\|_2\geq\|x\|_\infty[/tex] and substituting to get a suitable inequality, but no luck.
     
  2. jcsd
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