Grafiken erweitert

Linear Algebra Refresher.md

@@ -1,16 +1,54 @@
-Linear Algebra Refresher
+# Linear Algebra Refresher
 
-Addition von Vektoren
+## Grundgerüst
+
+```python
+# -*- coding: iso-8859-15 -*
+from math import sqrt
+
+class Vector(object):
+   def __init__(self, coordinates):
+      try:
+         if not coordinates:
+            raise ValueError
+         self.coordinates = tuple(coordinates)
+         self.dimension = len(coordinates)
+         
+      except ValueError:
+         raise ValueError('Die Koordinaten dürfen nicht leer sein')
+         
+      except TypeError:
+         raise TypeError('Die Koordinaten müssen iterierbar sein')
+                
+   def __str__(self):
+      return 'Vector: {}'.format(self.coordinates)
+  
+   def __eq__(self, v):
+      return self.coordinates == v.coordinates
+```
+
+## Addition von Vektoren
 
 $\left[ {\begin{array}{*{20}{c}}
-1\\
+5\\
-2
+0
 \end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
-3\\
+2\\
-1
+2
 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
-4\\
+7\\
-3
+2
 \end{array}} \right]$
 
-<img src="vektor_add.png" style="zoom:50%;" />
+```python
+veka1 = Vector([0,5])
+veka2 = Vector([2,2])
+
+print (veka1.plus(veka2))
+```
+
+<img src="vektor_add.png" style="zoom:40%;" />
+
+```python
+veka1 = Vector([0,5])
+```

Vek_Subt_1.tex

@@ -0,0 +1,43 @@
+\documentclass[10pt]{article}
+\usepackage{pgf,tikz,pgfplots}
+\pgfplotsset{compat=1.16}
+\usepackage{mathrsfs}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+
+\begin{document}
+
+
+\begin{tikzpicture}[x=1cm,y=1cm]
+
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+ymajorgrids=true,
+xmajorgrids=true,
+xmin=-1.4889190764182563,
+xmax=9.29392311219538,
+ymin=-2.7120035219099305,
+ymax=6.461032721583817,
+xtick={-1,-0.5,...,9},
+ytick={-2.5,-2,...,6},]
+
+\clip(-1.4889190764182563,-2.7120035219099305) rectangle (9.29392311219538,6.461032721583817);
+
+\draw [-latex,line width=2pt] (0,0) -- (4,1);
+\draw [-latex,line width=2pt,color=red] (0,0) -- (2,3);
+\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=orange] (4,1) -- (6,4);
+\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=orange] (2,3) -- (6,4);
+\draw [color=blue,-latex,line width=2pt] (0,0) -- (6,4);
+\begin{scriptsize}
+
+\draw[color=orange] (0.07325947387559195,0.1885048229954136) node {$A$};
+\draw[color=black] (2.949954121367923,2.350788548097263) node {$u$};
+\draw[color=black] (2.273645114838269,0.845762871594654) node {$v$};
+\draw[color=red] (0.8067213541964842,1.7697343312196734) node {$w$};
+\draw[color=orange] (5.350374820599933,2.5603490853318034) node {$a$};
+\draw[color=orange] (4.073960639262277,3.8558142245998717) node {$b$};
+\end{scriptsize}
+\end{axis}
+\end{tikzpicture}
+\end{document}

Vek_Subt_2.tex

@@ -0,0 +1,49 @@
+\documentclass[10pt]{article}
+\usepackage{pgf,tikz,pgfplots}
+\pgfplotsset{compat=1.16}
+\usepackage{mathrsfs}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+
+\begin{document}
+
+
+
+\begin{tikzpicture}[x=1cm,y=1cm]
+
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+ymajorgrids=true,
+xmajorgrids=true,
+xmin=-0.5,
+xmax=6.5,
+ymin=-1.5,
+ymax=3.5,
+xtick={-2,-1,...,7},
+ytick={-3,-2,...,7},]
+
+\clip(-2.362405497527683,-3.0044357261417667) rectangle (9.498720909947316,7.085904141701357);
+
+\draw [-latex,line width=2pt,color=red] (0,0) -- (6,2);
+\draw [-latex,line width=2pt, color=orange] (0,0) -- (1.5,3);
+\draw [-latex,line width=2pt,color=blue] (0,0) -- (4.5,-1);
+\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=blue] (1.5,3) -- (6,2);
+\draw [-latex,line width=1.2pt,dash pattern=on 1pt off 1pt,color=orange] (4.5,-1) -- (6,2);
+\begin{scriptsize}
+
+
+\draw[color=black] (2.9604321482296485,1.3910965423527197) node {$u$};
+
+
+\draw[color=orange] (0.5,1.852129724268709) node {$\vec{x}$};
+\draw[color=orange] (2.090755918706305,-0.18060748690633394) node {$w$};
+\draw[color=orange] (4.175883264189984,2.5751135777278735) node {$a$};
+\draw[color=orange] (5.1,0.8776732261280955) node {$\vec{x}'$};
+
+\end{scriptsize}
+\end{axis}
+
+\end{tikzpicture}
+
+\end{document}

Vektor_Laenge.tex

@@ -0,0 +1,44 @@
+\documentclass[10pt]{article}
+\usepackage{pgf,tikz,pgfplots}
+\pgfplotsset{compat=1.15}
+\usepackage{mathrsfs}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+\newcommand{\degre}{\ensuremath{^\circ}}
+\begin{document}
+\definecolor{qqwuqq}{rgb}{0,0.39215686274509803,0}
+\definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1}
+\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1}
+\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+ymajorgrids=true,
+xmajorgrids=true,
+xmin=-1.3544263878097484,
+xmax=9.691411951745668,
+ymin=-3.214189806288097,
+ymax=6.1825790285103785,
+xtick={-1,-0.5,...,9.5},
+ytick={-3,-2.5,...,6},]
+\clip(-1.3544263878097484,-3.214189806288097) rectangle (9.691411951745668,6.1825790285103785);
+\draw[line width=2pt,color=qqwuqq,fill=qqwuqq,fill opacity=0.10000000149011612] (8,0.20699436025945198) -- (7.793005639740548,0.206994360259452) -- (7.793005639740548,0) -- (8,0) -- cycle; 
+\draw [line width=2pt] (0,0)-- (8,0);
+\draw [line width=2pt] (8,0)-- (8,4);
+\draw [->,line width=2pt] (0,0) -- (8,4);
+\begin{scriptsize}
+\draw [fill=uuuuuu] (0,0) circle (2pt);
+\draw[color=uuuuuu] (0.07997134709718273,0.18640618429058298) node {$A$};
+\draw [fill=xdxdff] (8,0) circle (2.5pt);
+\draw[color=xdxdff] (8.081373677870541,0.2059217997314936) node {$B$};
+\draw[color=black] (4.031883473881585,-0.03802339327988945) node {$f$};
+\draw [fill=ududff] (8,4) circle (2.5pt);
+\draw[color=ududff] (8.081373677870541,4.206622965118176) node {$C$};
+\draw[color=black] (8.188709562795548,2.1184521129407368) node {$g$};
+\draw[color=qqwuqq] (8.315561063161468,0.18640618429058298) node {$\alpha = 90\textrm{\degre}$};
+\draw[color=black] (4.012367858440674,2.157483343822558) node {$u$};
+\end{scriptsize}
+\end{axis}
+\end{tikzpicture}
+\end{document}

Vektor_add_1.tex

@@ -0,0 +1,50 @@
+\documentclass[10pt]{article}
+\usepackage{pgf,tikz,pgfplots}
+\pgfplotsset{compat=1.15}
+\usepackage{mathrsfs}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+\begin{document}
+\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1}
+\definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1}
+\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+ymajorgrids=true,
+xmajorgrids=true,
+xmin=-4.66270591911281,
+xmax=11.894647164540304,
+ymin=-2.4761462907710943,
+ymax=7.830725732214009,
+xtick={-4,-3,...,11},
+ytick={-2,-1,...,7},]
+\clip(-4.66270591911281,-2.4761462907710943) rectangle (11.894647164540304,7.830725732214009);
+\draw [->,line width=2pt] (0,0) -- (5,2);
+\draw [->,line width=2pt] (0,0) -- (1,4);
+\draw [->,line width=2pt] (0,0) -- (5,2);
+\draw [->,line width=2pt] (0,0) -- (6,6);
+\draw [->,line width=2pt] (1,4) -- (6,6);
+\draw [->,line width=2pt] (5,2) -- (6,6);
+\begin{scriptsize}
+\draw [fill=uuuuuu] (0,0) circle (2pt);
+\draw[color=uuuuuu] (0.08937214755944764,0.20492478062845743) node {$A$};
+\draw [fill=ududff] (5,2) circle (2.5pt);
+\draw[color=ududff] (5.08761642038815,2.22776882252273) node {$B$};
+\draw[color=black] (2.5189255735382816,1.1681838481971587) node {$u$};
+\draw [fill=ududff] (1,4) circle (2.5pt);
+\draw[color=ududff] (1.0847398507137718,4.22920710735992) node {$C$};
+\draw[color=black] (0.49608153164401014,2.142145794294401) node {$v$};
+\draw [fill=ududff] (5,2) circle (2.5pt);
+\draw[color=ududff] (5.119725055973774,2.2598774581083534) node {$B_1$};
+\draw[color=black] (2.551034209123905,1.2002924837827822) node {$u_1$};
+\draw[color=black] (3.000555107322632,3.158919254505808) node {$w$};
+\draw [fill=xdxdff] (6,6) circle (2.5pt);
+\draw[color=xdxdff] (6.082984123542475,6.23064539219711) node {$D$};
+\draw[color=black] (3.524996155221147,5.171060417871539) node {$a$};
+\draw[color=black] (5.494325804472712,4.143584079131591) node {$b$};
+\end{scriptsize}
+\end{axis}
+\end{tikzpicture}
+\end{document}

Vektor_add_2.tex

@@ -0,0 +1,38 @@
+\documentclass[10pt]{article}
+\usepackage{pgf,tikz,pgfplots}
+\pgfplotsset{compat=1.15}
+\usepackage{mathrsfs}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+\begin{document}
+\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
+\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
+\begin{axis}[
+x=1cm,y=1cm,
+axis lines=middle,
+ymajorgrids=true,
+xmajorgrids=true,
+xmin=-3.5301370701590713,
+xmax=7.701311755516924,
+ymin=-3.410207869386736,
+ymax=6.144461052102637,
+xtick={-3.5,-3,...,7.5},
+ytick={-3,-2.5,...,6},]
+\clip(-3.5301370701590713,-3.410207869386736) rectangle (7.701311755516924,6.144461052102637);
+\draw [->,line width=2pt] (0,0) -- (7,2);
+\draw [->,line width=2pt] (0,0) -- (-3,2);
+\draw [->,line width=2pt] (0,0) -- (4,4);
+\draw [->,line width=2pt] (-3,2) -- (4,4);
+\draw [->,line width=2pt] (7,2) -- (4,4);
+\begin{scriptsize}
+\draw [fill=uuuuuu] (0,0) circle (2pt);
+\draw[color=uuuuuu] (0.08138887731978244,0.19635719080161987) node {$A$};
+\draw[color=black] (3.5242446569218764,1.1587693251572473) node {$u$};
+\draw[color=black] (-1.4862515064759836,1.0793951285093604) node {$v$};
+\draw[color=black] (2.0062131460310395,2.150946783255832) node {$w$};
+\draw[color=black] (0.5278687334641462,3.162967790516389) node {$a$};
+\draw[color=black] (5.5085995731190485,3.083593593868502) node {$b$};
+\end{scriptsize}
+\end{axis}
+\end{tikzpicture}
+\end{document}

vector.py

@@ -24,15 +24,15 @@ class Vector(object):
 	def __eq__(self, v):
 		return self.coordinates == v.coordinates
 		
-	#def plus(self,v):
-	#     new_coordinates = [x+y for x,y in zip(self.coordinates, v.coordinates)]
-	#     return Vector(new_coordinates)
-	
 	def plus(self,v):
-		new_coordinates =[]
+	    new_coordinates = [x+y for x,y in zip(self.coordinates, v.coordinates)]
-		n = len(self.coordinates)
+	    return Vector(new_coordinates)
-		for i in range(n):
+	
-			new_coordinates.append(self.coordinates[i] + v.coordinates[i])
+	#def plus(self,v):
+	#	new_coordinates =[]
+	#	n = len(self.coordinates)
+	#	for i in range(n):
+	#		new_coordinates.append(self.coordinates[i] + v.coordinates[i])
 			
 	def minus(self,v):
 		new_coordinates = [x-y for x,y in zip(self.coordinates, v.coordinates)]
@@ -57,22 +57,11 @@ class Vector(object):
 			
 # Tests
 
-vektor_1 = Vector([1,2,3])
-print (vektor_1)
 
-vektor_2 = Vector([1,2,3])
+veka1 = Vector([0,5])
-vektor_3 = Vector([-1,2,3])
+veka2 = Vector([2,2])
 
-print (vektor_1 == vektor_2)
+print (veka1.plus(veka2))
-print (vektor_2 == vektor_3)
 
-print (vektor_1.plus(vektor_2))
 
-print (vektor_2.minus(vektor_3))
-
-print (vektor_3.times_scalar(3))
-
-print ("Magnitude -- L<>nge ", vektor_3.magnitude())
-
-print ("Normalisieren ", vektor_2.normalized())