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# Numerical Mathematics
## Operator Norm
$$
||F||=\sup\limits_{x\neq0}\frac{||F(x)||_w}{||x||_v}=\sup\limits_{||x||_v=1}||F(x)||_w
$$
## Condition numbers
$K_a := Absolute condition number$
$K_r := Relative conditioon number$
### Operator linear
$$
K_a=||F||_{v,w}\in[0, \infin[
K_r\leq\frac{||F||_{v,w}}{\inf\limits_{||x||_v=1}||F(x)||_w}\in[0,\infin[
$$
### F, A bijektive
$$
K_r\leq||F||_{v,w}||F^{-1}||_{v,w}
K_r(A)=||A||_\infin||A^{-1}||_\infin
$$
### Component based
$$
K_r^c=||||
$$
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