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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.
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