Compute the condition number of the following matrix:
| 1 1 |
| E -E |
where E<<l infinity norm.
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!