302 lines
49 KiB
Text
302 lines
49 KiB
Text
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{
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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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"# Lineare Algebra Zusammenfassung"
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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": 30,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import Add, Matrix, Eq, Expr, MatMul, Mul, Equality, Equivalent, Function, Symbol, init_printing, latex\n",
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"from IPython.display import Markdown, Math\n",
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"init_printing(latex_printer=lambda *args, **kwargs: latex(*args, mul_symbol='dot', **kwargs))\n",
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"\n",
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"def calculate(vars: dict, calculation: Expr, precision: int = None):\n",
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" for key in vars:\n",
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" display(Eq(key, vars[key], evaluate=False))\n",
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"\n",
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" if isinstance(vars[key], Expr):\n",
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" display(Eq(key, vars[key].subs(vars, simultaneous=True), evaluate=False))\n",
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"\n",
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" display(Eq(calculation, calculation.subs(vars, simultaneous=True), evaluate=False))"
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]
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},
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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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"Linearer Spann im $\\mathbb{R}^2$\n",
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" - 2 Kollineare Vektoren \n",
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" Ursprungsgerade\n",
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" - 2 nicht-kollineare Vektoren $\\mathbb{R}^2$\n",
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"\n",
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"Im $\\mathbb{R}^3$\n",
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" - 3 kollineare Vektoren Ursprungsgerade\n",
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" - 3 komplanare, nicht-kollineare Vektoren \n",
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" Ursprungsebene\n",
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" - 3 linear unabhängige Vektoren \n",
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" $\\mathbb{R}^3$"
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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": 33,
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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": "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",
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"text/latex": [
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"$\\displaystyle M = \\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\end{matrix}\\right]$"
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],
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"text/plain": [
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" ⎡1 2 3⎤\n",
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"M = ⎢ ⎥\n",
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" ⎣4 5 6⎦"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": "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",
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"text/latex": [
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"$\\displaystyle N = \\left[\\begin{matrix}1 & 2\\\\3 & 4\\\\5 & 6\\end{matrix}\\right]$"
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],
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"text/plain": [
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" ⎡1 2⎤\n",
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" ⎢ ⎥\n",
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"N = ⎢3 4⎥\n",
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" ⎢ ⎥\n",
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" ⎣5 6⎦"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle M \\cdot N = \\left[\\begin{matrix}9 & 12 & 15\\\\19 & 26 & 33\\\\29 & 40 & 51\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" ⎡9 12 15⎤\n",
|
||
|
|
" ⎢ ⎥\n",
|
||
|
|
"M⋅N = ⎢19 26 33⎥\n",
|
||
|
|
" ⎢ ⎥\n",
|
||
|
|
" ⎣29 40 51⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"M = Symbol(\"M\")\n",
|
||
|
|
"N = Symbol(\"N\")\n",
|
||
|
|
"calculate({M: Matrix([[1, 2, 3], [4, 5, 6]]), N: Matrix([[1, 2], [3, 4], [5, 6]])}, M*N)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Die Funktionen $f: \\mathbb{R} \\rightarrow \\mathbb{R}: x \\mapsto m \\cdot x$ ($m \\in \\mathbb{R}$) sind lineare Abbildungen."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 10,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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",
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(x + y \\right)} = m \\cdot \\left(x + y\\right)$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"f(x + y) = m⋅(x + y)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"f = Function('f')\n",
|
||
|
|
"m = Symbol('m')\n",
|
||
|
|
"x = Symbol('x')\n",
|
||
|
|
"y = Symbol('y')\n",
|
||
|
|
"la = Symbol('\\lambda')\n",
|
||
|
|
"display(Eq(f(x + y), m * (x + y)))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(\\left[\\begin{matrix}x\\\\y\\\\z\\\\w\\end{matrix}\\right] \\right)} = \\left[\\begin{matrix}w + x\\\\- y + z\\\\- 2 \\cdot w - x + y\\\\2 \\cdot x - y\\\\w + z\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" ⎡ w + x ⎤\n",
|
||
|
|
" ⎛⎡x⎤⎞ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢ -y + z ⎥\n",
|
||
|
|
" ⎜⎢y⎥⎟ ⎢ ⎥\n",
|
||
|
|
"f⎜⎢ ⎥⎟ = ⎢-2⋅w - x + y⎥\n",
|
||
|
|
" ⎜⎢z⎥⎟ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢ 2⋅x - y ⎥\n",
|
||
|
|
" ⎝⎣w⎦⎠ ⎢ ⎥\n",
|
||
|
|
" ⎣ w + z ⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(\\left[\\begin{matrix}1\\\\0\\\\0\\\\0\\end{matrix}\\right] \\right)} = \\left[\\begin{matrix}1\\\\0\\\\-1\\\\2\\\\0\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" ⎡1 ⎤\n",
|
||
|
|
" ⎛⎡1⎤⎞ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢0 ⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
"f⎜⎢ ⎥⎟ = ⎢-1⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢2 ⎥\n",
|
||
|
|
" ⎝⎣0⎦⎠ ⎢ ⎥\n",
|
||
|
|
" ⎣0 ⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(\\left[\\begin{matrix}0\\\\1\\\\0\\\\0\\end{matrix}\\right] \\right)} = \\left[\\begin{matrix}0\\\\-1\\\\1\\\\-1\\\\0\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" ⎡0 ⎤\n",
|
||
|
|
" ⎛⎡0⎤⎞ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢-1⎥\n",
|
||
|
|
" ⎜⎢1⎥⎟ ⎢ ⎥\n",
|
||
|
|
"f⎜⎢ ⎥⎟ = ⎢1 ⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢-1⎥\n",
|
||
|
|
" ⎝⎣0⎦⎠ ⎢ ⎥\n",
|
||
|
|
" ⎣0 ⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(\\left[\\begin{matrix}0\\\\0\\\\1\\\\0\\end{matrix}\\right] \\right)} = \\left[\\begin{matrix}0\\\\1\\\\0\\\\0\\\\1\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" ⎡0⎤\n",
|
||
|
|
" ⎛⎡0⎤⎞ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢1⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
"f⎜⎢ ⎥⎟ = ⎢0⎥\n",
|
||
|
|
" ⎜⎢1⎥⎟ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢0⎥\n",
|
||
|
|
" ⎝⎣0⎦⎠ ⎢ ⎥\n",
|
||
|
|
" ⎣1⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle f{\\left(\\left[\\begin{matrix}0\\\\0\\\\0\\\\1\\end{matrix}\\right] \\right)} = \\left[\\begin{matrix}1\\\\0\\\\-2\\\\0\\\\1\\end{matrix}\\right]$"
|
||
|
|
],
|
||
|
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"text/plain": [
|
||
|
|
" ⎡1 ⎤\n",
|
||
|
|
" ⎛⎡0⎤⎞ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢0 ⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
"f⎜⎢ ⎥⎟ = ⎢-2⎥\n",
|
||
|
|
" ⎜⎢0⎥⎟ ⎢ ⎥\n",
|
||
|
|
" ⎜⎢ ⎥⎟ ⎢0 ⎥\n",
|
||
|
|
" ⎝⎣1⎦⎠ ⎢ ⎥\n",
|
||
|
|
" ⎣1 ⎦"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"x = Symbol('x')\n",
|
||
|
|
"y = Symbol('y')\n",
|
||
|
|
"z = Symbol('z')\n",
|
||
|
|
"w = Symbol('w')\n",
|
||
|
|
"f = Function('f')\n",
|
||
|
|
"\n",
|
||
|
|
"def realF(x, y, z, w):\n",
|
||
|
|
" return Matrix([x + w, z - y, y - x - 2 * w, 2 * x - y, z + w])\n",
|
||
|
|
"\n",
|
||
|
|
"display(Eq(f(Matrix([x, y, z, w])), realF(x, y, z, w), evaluate=False))\n",
|
||
|
|
"input = 1, 0, 0, 0\n",
|
||
|
|
"display(Eq(f(Matrix(input)), realF(*input), evaluate=False))\n",
|
||
|
|
"input = 0, 1, 0, 0\n",
|
||
|
|
"display(Eq(f(Matrix(input)), realF(*input), evaluate=False))\n",
|
||
|
|
"input = 0, 0, 1, 0\n",
|
||
|
|
"display(Eq(f(Matrix(input)), realF(*input), evaluate=False))\n",
|
||
|
|
"input = 0, 0, 0, 1\n",
|
||
|
|
"display(Eq(f(Matrix(input)), realF(*input), evaluate=False))"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"interpreter": {
|
||
|
|
"hash": "184a40b3dca75cecb3b866e2d98ad88cc8239a23b64498ef3e7e2e1f5f9f2635"
|
||
|
|
},
|
||
|
|
"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"
|
||
|
|
},
|
||
|
|
"orig_nbformat": 4
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 2
|
||
|
|
}
|