315 lines
188 KiB
Plaintext
315 lines
188 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "6fc01cbe-c0f2-47cf-9e63-d36025f14198",
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"metadata": {},
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"source": [
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"# Normen"
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]
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},
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{
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"attachments": {
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"d843217e-952b-46e6-8a43-0ab6e38fe50d.png": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAA5EAAAJUCAYAAACMgKIMAAAgAElEQVR4XuzdD/gVVX7n+cM+M5PQakRaoKcHiLb5kQch0E1w5YcYJAi6bSYgIG6L0YWff6DT8REwvTKwMd3Pj+BmFHvtTgMqONpqLwiIM+nZViDCiqALa7cEZAJPk25gTCMtYEdDMjs7Lt/qPbfPrXuq6lTdU/dW1X1fH5+k/dWtOvU6p+rWp07VOX0+Of9RfBBAAAEEEEAAAQQQQAABBBBwEOhDiHRQYhEEEEAAAQQQQAABBBBAAIFAgBBJQ0AAAQQQQAABBBBAAAEEEHAWIEQ6U7EgAggggAACCCCAAAIIIIAAIZI2gAACCCCAAAIIIIAAAggg4CxAiHSmYkEEEEAAAQQQQAABBBBAAAFCJG0AAQQQQAABBBBAAAEEEEDAWYAQ6UzFgggggAACCCCAAAIIIIAAAoRI2gACCCCAAAIIIIAAAggggICzACHSmYoFEUAAAQQQQAABBBBAAAEECJG0AQQQQAABBBBAAAEEEEAAAWcBQqQzFQsigAACCCCAAAIIIIAAAggQImkDCCCAAAIIIIAAAggggAACzgKESGcqFkQAAQQQQAABBBBAAAEEECBE0gYQQAABBBBAAAEEEEAAAQScBQiRzlQsiAACCCCAAAIIIIAAAgggQIikDSCAAAIIIIAAAggggAACCDgLECKdqVgQAQQQQAABBBBAAAEEEECAEEkbQAABBBBAAAEEEEAAAQQQcBYgRDpTsSACCCCAAAIIIIAAAggggAAhkjaAAAIIIIAAAggggAACCCDgLNCxIfKf1D+p//f8P3wQQAABBKot8Cn1qWrvIHuHAAIIIIBAiwU6NkS+p95Tf3f+Hz4IIIAAAtUWGK6Gn4+RBMlq1zJ7hwACCCDQSgFCZCu12RYCCCCAQMsFCJEtJ2eDCCCAAAIVFyBEVryC2T0EEECg0wUIkZ3eAth/BBBAAAHfAoRI36KsDwEEEECgUAKEyEJVB4VBAAEEEKiAACGyApXILiCAAAIIRAsQImkdCCCAAAII+BUgRPr1ZG0IIIAAAgUTIEQWrEIoDgIIIIBA6QUIkaWvQnYAAQQQQCBOgBBJ+0AAAQQQQMCvACHSrydrQwABBBAomAAhsmAVQnEQQAABBEovQIgsfRWyAwgggAAC9ETSBhBAAAEEEGidACGyddZsCQEEEECgDQL0RLYBnU0igAACCFRagBBZ6epl5xBAAAEECJG0AQQQQAABBPwKECL9erI2BBBAAIGCCRAiC1YhFAcBBBBAoPQChMjSVyE7gAACCCAQJ0CIpH0ggAACCCDgV4AQ6deTtSGAAAIIFEyAEFmwCqE4CCCAAAKlFyBElr4K2QEEEEAAAXoiaQMIIIAAAgi0ToAQ2TprtoQAAggg0AYBeiLbgM4mEUAAAQQqLUCIrHT1snMIIIAAAoRI2gACCCCAAAJ+BQiRfj1ZGwIIIIBAwQQIkQWrEIqDAAIIIFB6AUJk6avQ3w68f+J99beH/ladPH4yWOllwy9Tlw+/XF3U7yJ/G2FNpRR4a+tbau3ytUF76FnaowYOHtjS/Wj39lu6s2zMuwAh0jspK0QAAQQQ6HABQmQTDWD/nv1q8bTF6sypM6nW8rkRn1NfuPYL6urrr1Yjrx7Z8gvycGH//uzfq+888h21bvm6hv2YMnuKWrF+RfDf//26f6++3vP12jKXDLhEbT68uSUh88j+I3Vl6xrVlco8aWEJ0B+e/rC22MX9L257vSSVuRV/l7bxH57+D2rlopW1zf35xj9Xvzvzd1uxedXu7bvs5JJbl6itG7Y2LCrH+SMvPaKGdg11WY369rJv1x2D63avU6O6Rzl9l4XiBQiRtBAEEEAAAQT8ChAim/AMh6qsq5q3dJ6aNX9WW0KLXKQvnr5Yvb3zbWvxzRBpu1j+7jvfVb4DXbgg4Ytr+fufrP0T9fvzfj8red33JEB+ccgX6/5bKwOyl53wsBJpCz899lN17uNz6seHfqwO7j2oNq3e1LBmn/bmytu9/ayEY/uMjfyqefwkrT+8nryck8pRxb8TIqtYq+wTAggggEA7BQiRTej7CpFSBAktj778aMt7Hv5q01+pr876ap2C9DRd+tlL1beWfEt9etCnaz2R7QqRtu2muThPqmLp5fzS6C81LNaKgJxUtlb+PapHLVyGvMJNu7ef1TouRMo6/+LVv1BXT7k6cfWEyESizAsQIjPT8UUEEEAAAQSsAoTIJhqGLUSOmThG/fHjfxy51kP7Dqm/fPYvI3v+XC84myh23VfDF+7yCN6GAxuCZaSHbtuL29RtC28L/ndZQqR+NNX1kVRC5C+axOyRs9XRg0cTm1ZeIbLd20/c8YgFkkKkeUzFbYMQmbUGkr9HiEw2YgkEEEAAAQTSCHgLkf+g/iHNdtu+7Cl1Sv3s/D/NfGwh0rWHTILLl6//csP7lNIj+fzbz7fs0dbwhWtc+WVwk2VzltXKLMv+mzX/Jvd3IuXd03nj59VVVdT7Yi889kLd+3uLVi6qheC4ur7nunvqgr3cDHhixxPNNI/SfVc/TqoL/pmhn1F/du+fNbzvl1eIbPf2s1ZY+BiSYzj8nrTLzSFCZNYaSP7e5epy9avn/+GDAAIIIIAAAu4C/1z94h/bx0uI/ER9ot4+/0+nfZoJkWJ17Mgx1XNNT8MF58z5M9WSVUtawpkmRLakQE1uJNxb6hrqm9xsZb9u633OK0TaENu9fZeKDR9DcuPi6RVP1x3XLr2RhEgXbZZBAAEEEEAAgVYJ9Ff9z9+GvZwQ6Ru82RAp5ZHevT+c+ocNRfuPx/9jS3ojCZG+W0W11tfuENfu7bvUpi38yffMkYzlfyf1RhIiXbRZBgEEEEAAAQRaJUCIzEnaR4iUotneBWtVbw8hMqfGUZHVtjvEtXv7LtUYFf7Cx3VSbyQh0kWbZRBAAAEEEECgVQKEyJykfYXI8Ht8UlyXxzBlAJkDbx0I3ln74OQHwTt98j7W2Elj1W+N+y111eSrIqff0O+fhUclDQ8MFJ6+w5yvMWrgGuldPXn8ZKB+4cUXBuW4qN9FtVqQdxxlCok9r+wJ/lv3Dd1q+NjhsVOFyKO//3Tun4Llf6XvrzTMvaf//m/v+7cN7zaGBzqSd/3M8sg6be/jhZcJNyPZj13f26WOHzmu9r22L3h8UYLCFSOuSPTX6xJPGWxJf8ZNHVfXAy379cPXfxhMt/Hz0z8P1nvFyCucRvv00ezbHeKa2X64TsXDdbClNHZR4c/2lEFcb2TWENlsO9THo+14FcO92/eqt7a9pUZcNaI2rY7+7x99+FFANWjIoLo2qf/+n37wn4Lj49f6/1rw/XD71s5ShgNvHlB//eZf184Jlw2/rOWjVaepd5ZFAAEEEECg6gKEyJxq2FeIjHqkdd8n+6wlt03AHrWLUYPfTBk4peFdTNs6zPczw/trGwRIQs+MYTPqVqUnp5fAtPS2pZEjgMp8mV/u/XJDMWwD65jTb0T5RZnYBs0JD6wTF+KT9sPcbtKE8+F60N5yg+CxxY9ZJ7GX9cs+PLrl0dwHNWomxPk47JrZvm3U3Tx6+OPCn603cu2utdZ6SxsifbRD2xyp+niVY/mBmx+oHa/mMWGbGmjz4c3BzR3524oFKyLPL2aQDm8j3GZaNXiXj7bKOhBAAAEEEKiaACEypxr1FSKjppiwhUgJkIunL26YIkT3QOoeSXOXw4FD1jHpkklOKmaIdJniI+rCXXoVwiOs2gpgu8i3OZvL2S5o43bO9lihbZoGm39UYBVjmVPzRwd/1BCS4+YAtT1OvPDRhWrOmDmJId+lt9qpkmMWaibENbtt+X4z2y9CiLS1l6ggmyZE+mqHUUafv/bzDYN+me3NdkzKjR3pVQ+/C2prB7KsPFFgG1gsvHzUzSUf7Yt1IIAAAggggEC0ACEyp9aRd4i0TXYvd/g3rd5Ut0e650D/R+ldWHb7srqgGZ7qQj8K+9VZX23QkYtc+cgjaldedWWt1yRriNSjVV5+5eXqKyu+UntE7dvLvq3WLV9Xt31bL2FSiJQV6Efywhew
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}
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},
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"cell_type": "markdown",
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"id": "9c937dc2-2946-4835-bf9c-c53a0337e869",
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"metadata": {},
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"source": [
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""
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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": 2,
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"id": "0efc8c51-d7ee-4912-92a6-c3c0f93b4895",
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"metadata": {},
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"outputs": [],
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"source": [
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"from math import sqrt\n",
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"\n",
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"def l1(x: list[float]) -> float:\n",
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" a=0\n",
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" for i in x:\n",
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" a+= abs(i)\n",
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" return a\n",
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"\n",
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"def l2(x: list[float]) -> float:\n",
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" a=0\n",
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" for i in x:\n",
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" a+= i**2\n",
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" return sqrt(a)\n",
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"\n",
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"def li(x: list[float]) -> float:\n",
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" return max(x)\n"
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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": 24,
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"id": "a96e8b6e-563d-4a3c-9f74-865f19f69884",
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"metadata": {},
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"outputs": [],
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"source": [
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"from IPython.display import display, Math, Latex\n",
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"\n",
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"def norms(x: list[float]):\n",
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" display(Math(f\"$x = {x}$\"))\n",
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" display(Math(f\"$||x||_{{l1}} = {l1(x)}$\"))\n",
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" display(Math(f\"$||x||_{{l2}} = {l2(x)}$\"))\n",
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" display(Math(f\"$||x||_{{l \\\\infty}} = {li(x)}$\"))"
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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": 26,
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"id": "d98ecf8f-0a20-4914-b183-a5a1ed347058",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle x = (1, 3, 2)$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l1} = 6$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l2} = 3.7416573867739413$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l \\infty} = 3$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle x = (20, 3, 2)$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l1} = 25$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l2} = 20.322401432901575$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"text/latex": [
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"$\\displaystyle ||x||_{l \\infty} = 20$"
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],
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"text/plain": [
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"<IPython.core.display.Math object>"
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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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"source": [
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"x = (1,3,2)\n",
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"norms(x)\n",
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"x = (20,3,2)\n",
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"norms(x)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "689e658e-1eb5-4e1a-93f4-82b0fa065eb9",
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"metadata": {},
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"source": [
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"# Metriken"
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]
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},
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{
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"attachments": {
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"87611157-5376-4e9d-bc57-bc2072304dc7.png": {
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|
|
"image/png": "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
|
||
|
|
},
|
||
|
|
"ecffa3c8-4a1b-4041-99eb-dea0676bc39c.png": {
|
||
|
|
"image/png": "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
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "ec76ba02-f936-454e-9096-9aa0ce248091",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"---\n",
|
||
|
|
"\n",
|
||
|
|
""
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 86,
|
||
|
|
"id": "dddde255-6445-4913-b2c6-036331b4d318",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import numpy as np\n",
|
||
|
|
"def distance(x: list[float], y: list[float], norm = l2) -> float:\n",
|
||
|
|
" return abs(norm(np.array(x) - np.array(y)))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 95,
|
||
|
|
"id": "0a0172b2-c513-4ad4-adb2-509146773140",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle a = (1, 2, 3)$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"<IPython.core.display.Math object>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle b = (2, -1, 5)$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"<IPython.core.display.Math object>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle d(a,b) = 3.7416573867739413$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"<IPython.core.display.Math object>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle d(a,b)_{L1} = 6$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"<IPython.core.display.Math object>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle d(a,b)_{L1\\infty} = 3$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"<IPython.core.display.Math object>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"a = (1,2,3)\n",
|
||
|
|
"b = (2,-1,5)\n",
|
||
|
|
"display(Math(f\"$a = {a}$\"))\n",
|
||
|
|
"display(Math(f\"$b = {b}$\"))\n",
|
||
|
|
"display(Math(f\"$d(a,b) = {distance(a,b)}$\"))\n",
|
||
|
|
"display(Math(f\"$d(a,b)_{{L1}} = {distance(a,b, norm=l1)}$\"))\n",
|
||
|
|
"display(Math(f\"$d(a,b)_{{L\\\\infty}} = {distance(a,b, norm=li)}$\"))"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3 (ipykernel)",
|
||
|
|
"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": "3.12.2"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|