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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-/output/
+*output/*
+*.jpg
 # Created by https://www.gitignore.io/api/vim,linux,latex
 # Edit at https://www.gitignore.io/?templates=vim,linux,latex
 
diff --git a/README.md b/README.md
index b69d00c..1834331 100644
--- a/README.md
+++ b/README.md
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 # Lernzettel
 
+## Über das Projekt
+
+Dies ist eine Sammlung meiner Lernzettel für diverse Kurse.
+Da es ein Projekt von Studenten für Studenten ist, besteht keine Garantie auf Korrektheit oder Vollständigkeit.
+
+## About
+
+This is a collection of my digital lecture summaries.
+This being a full project by students for students, there is no guarantee for correctness and completeness.
+
 ## Inhaltsverzeichnis
 
 ### Einführung in die Informationssicherheit
 
-- [Source](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md)
-- [HTML](http://encrox.com/introduction_to_information_security.html)
+- [Quelldaten](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md)
+- [HTML](http://encrox.com/projects/lernzettel/introduction_to_information_security.html)
 - [PDF](http://encrox.com/introduction_to_information_security.pdf)
 
+### Numerische Mathematik
+
+- [Quelldaten](en_GB/Numerical Mathematics/numerical_mathematics.md)
+- [HTML](http://encrox.com/numerical_mathematics.html)
+- [PDF](http://encrox.com/numerical_mathematics.pdf)
+- [Klausurzettel](en_GB/Numerical Mathematics/cheatsheet.jpg)
+
 ## Table of contents
 
 ### Introduction to Information Security
@@ -15,3 +32,10 @@
 - [Source](en_GB/Introduction to Information Security/introduction\_to\_information\_security.md)
 - [HTML](http://encrox.com/introduction_to_information_security.html)
 - [PDF](http://encrox.com/introduction_to_information_security.pdf)
+
+### Numerical Mathematics
+
+- [Source](en_GB/Numerical Mathematics/numerical_mathematics.md)
+- [HTML](http://encrox.com/numerical_mathematics.html)
+- [PDF](http://encrox.com/numerical_mathematics.pdf)
+- [Cheatsheet](en_GB/Numerical Mathematics/cheatsheet.jpg)
diff --git a/en_GB/Numerical Mathematics/numerical_mathematics.md b/en_GB/Numerical Mathematics/numerical_mathematics.md
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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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