# Condition Number

1. May 5, 2007

### DeadxBunny

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
A=
| 1 1 |
| E -E |

A^-1=
| 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. May 5, 2007

### lalbatros

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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