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01001 - Matematik 1a/Noter/Andenordens differentialligninger/python-mobius.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8d87a703",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sympy as sp\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "dffe7f14",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}52 & -8 & -8\\\\-4 & 50 & 2\\\\-4 & 2 & 50\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[52, -8, -8],\n",
+       "[-4, 50,  2],\n",
+       "[-4,  2, 50]])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{60: 1, 48: 1, 44: 1}\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Opgave 1\n",
+    "A = sp.Matrix([[52, -8, -8], [-4, 50, 2], [-4, 2, 50]])\n",
+    "display(A)\n",
+    "eigenvalsA = A.eigenvals()\n",
+    "print(eigenvalsA)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "debdde8b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}9 & -2 & 1\\\\-1 & 10 & -1\\\\1 & -2 & 9\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([\n",
+       "[ 9, -2,  1],\n",
+       "[-1, 10, -1],\n",
+       "[ 1, -2,  9]])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[(8, 2, [Matrix([\n",
+      "[2],\n",
+      "[1],\n",
+      "[0]]), Matrix([\n",
+      "[-1],\n",
+      "[ 0],\n",
+      "[ 1]])]), (12, 1, [Matrix([\n",
+      "[ 1],\n",
+      "[-1],\n",
+      "[ 1]])])]\n",
+      "hej\n",
+      "Matrix([[2], [1], [0]])\n",
+      "Matrix([[-1], [0], [1]])\n",
+      "Matrix([[1], [-1], [1]])\n",
+      "Matrix([[12], [20], [-20]])\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Opgave 2\n",
+    "\n",
+    "B = sp.Matrix([[9, -2, 1], [-1, 10, -1], [1, -2, 9]])\n",
+    "display(B)\n",
+    "eigenvectsB = B.eigenvects()\n",
+    "\n",
+    "print(eigenvectsB)\n",
+    "print(\"hej\")\n",
+    "print(eigenvectsB[0][2][0])\n",
+    "print(eigenvectsB[0][2][1])\n",
+    "print(eigenvectsB[1][2][0])\n",
+    "\n",
+    "print(sp.Matrix([[9, -2, 1], [-1, 10, -1], [1,-2,9]]) * sp.Matrix([2, 2, -2]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fa460b84",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Opgave 3\n",
+    "\n"
+   ]
+  }
+ ],
+ "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": "3.13.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}