88 lines
3.8 KiB
Plaintext
88 lines
3.8 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Aufgaben\n",
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"Gegeben ist die folgende lineare Abbildung:\n",
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"$$f: \\mathbb{R}^2 \\rightarrow \\mathbb{R}^3:\n",
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"\\begin{pmatrix}\n",
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"x_1 \\\\\n",
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"x_2\n",
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"\\end{pmatrix}\n",
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"\\mapsto\n",
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"\\begin{pmatrix}\n",
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"-x_2 \\\\\n",
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"2x_1 \\\\\n",
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"x_2 - x_1\n",
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"\\end{pmatrix}$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import init_printing, latex, Symbol, Function, Matrix, Eq, Mul, MatMul\n",
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"init_printing(latex_printer=lambda *args, **kwargs: latex(*args, mul_symbol='dot', **kwargs))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAAAzCAYAAABlnH0mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFWUlEQVR4Ae2c7VFVMRCGkaEARzvADlAqUDsQOkA70OEf/xjsAKxAsQOwAoUOtAORDvB9YnI4Nydf957cIxeyM7nJ2Wx2k93s5ovh0c3NzVqDxTRwcHDwONRS+OsQPoSL8VgPETdcsQYuRPnHS0fFrf8Rnnrt4Xe6MSeTRj7UwGvN+vMhugyjtq/7lPp+q++d5jF9rdyhcvOYCYwhL9iSGELWc5WL1p9mmCUZRgZgY/BJ6UrphdKmUjE0wxSraj5C6xk7tFL5vTK8phjaGlOsqmkJm2Gm1XextGaYYlVNS9gMM62+i6U1wxSralrCZphp9V0srRmmWFXTEjbDTKvvYmlVDKMD1GaxxDkIl8V3ji78N9LRhlnkVOuPVjy4RwrBpuUfqlsl3FPb2SelnU4aRko5VjqyafAoJPwbCXqq/GupwAjdY/F45dcJZ67TlXMVvnKgfp+S1HHXf/NdMp7oXZka8+CDhY+Vvil9V+oMoHoMta/8ufIkWFoelWLgQuHgXUNtPypdKH1RKrqZjQmZGq/+mruyReRGDSNmWHlPCeP8UPKVhuEwWhasQp+FCFXHBd92ZhDIQd67EI/7iAuGMimJsIJHnKtM4pXOn627wp1UUAr8kzPLykEefXoQEDSMRs5z5y8pwjeGUYrwrC2/zMfIH/G6LGSBvN1C2pUnmwllUhLhC6PgMVf6ZuEi90MINH5oE+oW1IbZva/022IJZR+EDxrb0qQy5CG3hpem5NyJOt8wDPpEyuNvmg6Vf4z0khe56PqidhiW+h2VjUco56EIQ31QWgR+qhF8syBZyC6i7TG7VLtkSO3RLr04YxikqXPRHVKvN3gDT6YDsO3PVPFO5X6YQlHgO1A9fAhP0OZ2d8hzfet4hAri5Xt4iOxO4waGUW+Z2WsaXF+p/iDYqcVCkvMkzibsuAAOWGf67sKfyshxsxoD5YA1poQux2cl6kOG2VbPxyzsKPurFB8Lg0YxqsfwhA82EiWQmgwl7VeKJmQYZnLKWxggYSU1ezmM1gbkITcLMvb9W2M0ahb2w8zo8ahYvKfO3Q3NsME7lLrbg5nK/AceU+TJknG/1hgNCGUzM3MeQz0hLwSDE7r4whM8aVFgc5Dr16K8l9ZOY3dj5tjAkYG7x+wE80MZYWxNDbtFmu8AfBaOM84A1JbtNgs/HWKLC/A9dhazdo3lYToz1Y/GzP0gxw4TJZQzQbn34yYlaRzfMBzgsqFGTFm015S2KPsDFS658Pv0uW/xM2FTeW7C5FhNVq++clhnQnb6VPnafrMGousorIuQuO9mP+sL3lACeMRUM5hDKfJWCTisDiatcGyMXknneE8U1lXDgLGsIVTeWTjaShWi45aAhywzm1O0oTraKSF73/Ih9rpzT9fE8od21a5iCL1X3UBuCy6EUR8FQpkxjM3nvZKAHm9LuqXqByBF08GS6xncfirPHPRzEYTGlvQGy5NdZhQ2xsxEtSVmcp3yXqnqukKP4asM/m6WRQdyxyqc0q8T/UoaD48ZBVZp1Y1Cp8R7KXxHDbhe4+BZz7FnjWlQXwOhtcVJcd7knkMcfiZvhplRR50PeboLYaFw5XDJ8NwMU8cWIS6cuUI7VucxyTNZM0xIpXVw7FY5F/pgrpZ6XuXXm+9mmKBaxiOleM5dPMt3zxoqE8Z4GNzLSRi9K8sJeOD1eAcHZy58WezJX+o7dCOgqltohrnVRfWSDMAmYKHDcQtl1c1Rh2EzTB09VufSDFNdpXUYNsPU0WN1Ls0w1VVah2HblY3XI29F7prFcLO7sSLOfls1MryaxxSpL0nEe1H/n8nN+9LKDcGg/V9o45EP0mnbbAAAAABJRU5ErkJggg==",
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"text/latex": [
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"$\\displaystyle f{\\left(\\vec{e_1} \\right)} = \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]$"
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],
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"text/plain": [
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" ⎡1⎤\n",
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"f(\\vec{e_1}) = ⎢ ⎥\n",
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" ⎣0⎦"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f = Function('f')\n",
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"e = Symbol('\\\\vec{e_1}')\n",
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"M = Matrix([1, 0])\n",
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"Eq(f(e), M, evaluate=False)"
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]
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}
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],
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"metadata": {
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"interpreter": {
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"hash": "341c8103277e0717e088b7bc94c2655a933f4146b751d7557e6ec751ee6c0dd9"
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},
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"kernelspec": {
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"display_name": "Python 3.10.2 ('ZHAW-Pb88adSo')",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.2"
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},
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"orig_nbformat": 4
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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