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Proving induced 1-norm.

  1. Jan 4, 2014 #1
    1. The problem statement, all variables and given/known data
    I'd like to show that the induced 1-norm satisfies: ∥A∥1=max1≤j≤n∑[i=1 to n] |ai,j|

    2. Relevant equations

    3. The attempt at a solution
    I realise the sum ∑[i=1 to n] |ai,j| is basically ||Ax|| where x is the j-th basis. I also know that ||A||1=max||x||1=1||Ax||. And since ||x||1=1, ∑[i=1 to n]|xi|=1.
    But I am not sure how to assemble all that together. Would anyone please advise?
  2. jcsd
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