1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proving induced 1-norm.

  1. Jan 4, 2014 #1
    Hi,
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted