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Matrix norms

  1. Oct 18, 2008 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations


    3. The attempt at a solution
    I think it is crucial that [itex] ||x||_1=1[/tex] but I don't see how I can use that info. Can someone help me?
  2. jcsd
  3. Oct 18, 2008 #2
    Try to show
    ||A||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
    ||A||_1 \leq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
    separately. Can you prover either of these statements?

    Hint: For the first one it is enough to find an x with norm one such that
    ||Ax||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
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