DeadxBunny

05-05-2007, 02:36 AM

Original Question:

Compute the condition number of the following matrix:

| 1 1 |

| E -E |

where E<<l infinity norm.

Relevant Equations:

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

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

My attempt:

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 K(A) correct or am I completely off? Any help is appreciated! Thanks!

Compute the condition number of the following matrix:

| 1 1 |

| E -E |

where E<<l infinity norm.

Relevant Equations:

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

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

My attempt:

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 K(A) correct or am I completely off? Any help is appreciated! Thanks!