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!

Condition Number

  1. May 5, 2007 #1
    1. The problem statement, all variables and given/known data
    Compute the condition number of the following matrix:

    | 1 1 |
    | E -E |

    where E<<l infinity norm.

    2. Relevant equations

    l infinity norm: ||x||infinity = max |xi| where i goes from 1 to n.

    Condition number: K(A) = ||A||*||A^-1||

    3. The attempt at a solution
    | 1 1 |
    | E -E |

    | 1 -E |
    | -1 -E |

    ||A||infinity = max(2,0) = 2
    ||A^-1||infinity = max(1-E,-1-E) = 1-E

    K(A) = 2(1-E) = 2-2E

    Is this right or am I completely off? Thanks!
  2. jcsd
  3. May 5, 2007 #2
    Your result for A^-1 is wrong.
    Additionally, you gave the definition for the norm of a vector but explained nothing concerning the norm of matrix. You should also explain how you calculated the norm of A and A^-1.
    The end result is wrong of course.
    It should be clear that the condition number increases a lot when E goes to zero.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook