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Homework Help: Matrix norms

  1. Oct 18, 2008 #1
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 18, 2008 #2
    Try to show
    [tex]
    ||A||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
    [/tex]
    and
    [tex]
    ||A||_1 \leq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
    [/tex]
    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
    [tex]
    ||Ax||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}
    [/tex]
     
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