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: 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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook