From f65ec3a75070feb4f19ed64b1afade68f50e6456 Mon Sep 17 00:00:00 2001
From: Leonard Kugis <leonard@kug.is>
Date: Tue, 21 Apr 2020 00:34:24 +0200
Subject: Numerical Mathematics

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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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