{
 "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,
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}