{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aufgaben\n",
    "Gegeben ist die folgende lineare Abbildung:\n",
    "$$f: \\mathbb{R}^2 \\rightarrow \\mathbb{R}^3:\n",
    "\\begin{pmatrix}\n",
    "x_1 \\\\\n",
    "x_2\n",
    "\\end{pmatrix}\n",
    "\\mapsto\n",
    "\\begin{pmatrix}\n",
    "-x_2 \\\\\n",
    "2x_1 \\\\\n",
    "x_2 - x_1\n",
    "\\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import init_printing, latex, Symbol, Function, Matrix, Eq, Mul, MatMul\n",
    "init_printing(latex_printer=lambda *args, **kwargs: latex(*args, mul_symbol='dot', **kwargs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle f{\\left(\\vec{e_1} \\right)} = \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "               ⎡1⎤\n",
       "f(\\vec{e_1}) = ⎢ ⎥\n",
       "               ⎣0⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = Function('f')\n",
    "e = Symbol('\\\\vec{e_1}')\n",
    "M = Matrix([1, 0])\n",
    "Eq(f(e), M, evaluate=False)"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "341c8103277e0717e088b7bc94c2655a933f4146b751d7557e6ec751ee6c0dd9"
  },
  "kernelspec": {
   "display_name": "Python 3.10.2 ('ZHAW-Pb88adSo')",
   "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": "3.10.2"
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  "orig_nbformat": 4
 },
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}