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: Find a norm on R2

  1. Nov 16, 2012 #1
    1. The problem statement, all variables and given/known data
    find a norm on R2 for which||(0,1)||=1=||(1,0)|| but ||(1,1)||=0.000001

    2. Relevant equations
    hints: ||(a,b)|| = A |a+b|+B|a-b

    3. The attempt at a solution
    by the hints i have A+B=1 and 2A=0.000001
    then solved the equations system i get A=0.0000005 B=1-A=0.9999995 then ||(a,b)|| = 0.000001|a+b|+0.9999995 |a-b|

    is it the answers???
  2. jcsd
  3. Nov 16, 2012 #2


    Staff: Mentor

    Yes, these values satisfy the given conditions.
  4. Nov 16, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Another solution would be to use a p-norm:
    [tex]||(a,b)|| = (a^p + b^p)^{1/p}[/tex]
    with [itex]p \geq 1[/itex]. This will satisfy [itex]||(1,0)|| = ||(0,1)|| = 1[/itex] for any [itex]p[/itex], so all you have to do is solve for the [itex]p[/itex] which gives the desired result for [itex]||(1,1)||[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook