diff --git a/M1_LineareAbbildungen.ipynb b/M1_LineareAbbildungen.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..5f92334fc546209f56a79c3340630e8cfec4e32e
--- /dev/null
+++ b/M1_LineareAbbildungen.ipynb
@@ -0,0 +1,202 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Importieren der nötigen Bibliotheken"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import math\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Definition der Punktemenge** (Eckpunkte der folgenden Figur):\n",
+    "* Die Punkte werden zunächst als Zeilen einer $n \\times 2$-Matrix $P$ definiert.\n",
+    "* Danach werden diese Matrix zu einer $2\\times n$- Matrix transponiert $P \\rightarrow P^T$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#points =[[0,2],[0,-2],[3,0],[3,2],[4,3],[5,2],[-1,3]]\n",
+    "points =[[0,2],[1,-2],[3,0]]\n",
+    "points = np.transpose(points)\n",
+    "\n",
+    "# Plotten als Punkte\n",
+    "plt.plot(points[0],points[1],'bo')\n",
+    "# Plotten des Polygons\n",
+    "plt.fill(points[0],points[1],facecolor = (0,.2,1,.7))\n",
+    "\n",
+    "# Einrichten des Plots\n",
+    "plt.axis('equal') # gleiche Skalierung x,y\n",
+    "plt.grid('both')  # Gitterlinien"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Definition der finalen Abbildungsmatrix** $A$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "S=[[-1,0],[0,1]]                           # Spiegelung\n",
+    "M=[[4,0],[0,.5]]                           # Skalierung  \n",
+    "R= math.sqrt(2)/2*np.array([[1,1],[-1,1]]) # Drehung\n",
+    "\n",
+    "A = S\n",
+    "#A=np.matmul(M,S)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Anwenden der Abbilungsmatrix**, d.h. für jeden Ortsvektor $\\vec v$ wird $$\\vec v \\mapsto A \\cdot \\vec v$$ ausgeführt."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# transformierten Punkte\n",
+    "pointsTransformed = np.matmul(A,points)\n",
+    "plt.plot(pointsTransformed[0],pointsTransformed[1],'yo')\n",
+    "plt.fill(pointsTransformed[0],pointsTransformed[1],facecolor = (1,.7,0,.7))\n",
+    "\n",
+    "# zum Verleich nochmal die ursprünglichen Punkte\n",
+    "plt.plot(points[0],points[1],'bo')\n",
+    "# Plotten des Polygons\n",
+    "plt.fill(points[0],points[1],facecolor = (0,.2,1,.7))\n",
+    "\n",
+    "# Einrichten des Plots\n",
+    "plt.axis('equal') # gleiche Skalierung x,y\n",
+    "plt.grid('both')  # Gitterlinien"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Durch Hinzufügen einer Translation $\\vec t$ wird die lineare Abbildung zu einer **affinen Abbildung**\n",
+    "$$\n",
+    "\\vec v \\mapsto A\\cdot \\vec v + \\vec t\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "t=np.transpose([[5,2]])\n",
+    "pointsAffine = pointsTransformed + t      #elementweise Addition des Vektors t\n",
+    "plt.fill(pointsAffine[0],pointsAffine[1], facecolor = (1,0,.5,.5))\n",
+    "\n",
+    "### die alten Figuren\n",
+    "pointsTransformed = np.matmul(A,points)\n",
+    "plt.plot(pointsTransformed[0],pointsTransformed[1],'yo')\n",
+    "plt.fill(pointsTransformed[0],pointsTransformed[1],facecolor = (1,.7,0,.7))\n",
+    "\n",
+    "# zum Verleich nochmal die ursprünglichen Punkte\n",
+    "plt.plot(points[0],points[1],'bo')\n",
+    "# Plotten des Polygons\n",
+    "plt.fill(points[0],points[1],facecolor = (0,.2,1,.7))\n",
+    "\n",
+    "# Einrichten des Plots\n",
+    "plt.axis('equal') # gleiche Skalierung x,y\n",
+    "plt.grid('both')  # Gitterlinien"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}