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
Ka := Absoluteconditionnumber
Kr := Relativeconditioonnumber
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
Krc = ||||