2023-10-29 02:06:02 +01:00
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "08d1226c-5a91-4675-84fe-34b299c3c82f",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[13285.201849510713, -26578.19232421982, 9516.240080329559]\n"
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]
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}
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],
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"source": [
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"using DelimitedFiles\n",
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"# https://docs.julialang.org/en/v1/stdlib/DelimitedFiles/\n",
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"\n",
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2023-11-15 11:23:16 +01:00
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"M = convert(Matrix{Int}, readdlm(\"salaries.csv\", ',', skipstart=1)[:, 2:end])\n",
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2023-10-29 02:06:02 +01:00
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"\n",
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2023-11-15 11:23:16 +01:00
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"A = M[1:end, 1:3]\n",
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"y = M[1:end, 4]\n",
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"x = A \\ y\n",
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2023-10-29 02:06:02 +01:00
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"\n",
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"println(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": 2,
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"id": "e7b91a49-8da1-4637-9336-d33e089f82c3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"<path clip-path=\"url(#clip400)\" d=\"M50.9921 1209.27 L80.6679 1209.27 L80.6679 1213.21 L50.9921 1213.21 L50.9921 1209.27 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M90.8067 1191.54 L109.163 1191.54 L109.163 1195.47 L95.0891 1195.47 L95.0891 1203.95 Q96.1076 1203.6 97.1261 1203.44 Q98.1447 1203.25 99.1632 1203.25 Q104.95 1203.25 108.33 1206.42 Q111.709 1209.59 111.709 1215.01 Q111.709 1220.59 108.237 1223.69 Q104.765 1226.77 98.4456 1226.77 Q96.2697 1226.77 94.0012 1226.4 Q91.7558 1226.03 89.3484 1225.29 L89.3484 1220.59 Q91.4317 1221.72 93.6539 1222.28 Q95.8761 1222.83 98.353 1222.83 Q102.358 1222.83 104.696 1220.73 Q107.033 1218.62 107.033 1215.01 Q107.033 1211.4 104.696 1209.29 Q102.358 1207.19 98.353 1207.19 Q96.478 1207.19 94.603 1207.6 Q92.7512 1208.02 90.8067 1208.9 L90.8067 1191.54 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M99.765 858.599 Q96.1539 858.599 94.3252 862.164 Q92.5197 865.705 92.5197 872.835 Q92.5197 879.941 94.3252 883.506 Q96.1539 887.048 99.765 887.048 Q103.399 887.048 105.205 883.506 Q107.033 879.941 107.033 872.835 Q107.033 865.705 105.205 862.164 Q103.399 858.599 99.765 858.599 M99.765 854.895 Q105.575 854.895 108.631 859.502 Q111.709 864.085 111.709 872.835 Q111.709 881.562 108.631 886.168 Q105.575 890.751 99.765 890.751 Q93.9549 890.751 90.8762 886.168 Q87.8206 881.562 87.8206 872.835 Q87.8206 864.085 90.8762 859.502 Q93.9549 854.895 99.765 854.895 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M90.8067 519.502 L109.163 519.502 L109.163 523.437 L95.0891 523.437 L95.0891 531.909 Q96.1076 531.562 97.1261 531.4 Q98.1447 531.215 99.1632 531.215 Q104.95 531.215 108.33 534.386 Q111.709 537.557 111.709 542.974 Q111.709 548.553 108.237 551.654 Q104.765 554.733 98.4456 554.733 Q96.2697 554.733 94.0012 554.363 Q91.7558 553.992 89.3484 553.252 L89.3484 548.553 Q91.4317 549.687 93.6539 550.242 Q95.8761 550.798 98.353 550.798 Q102.358 550.798 104.696 548.691 Q107.033 546.585 107.033 542.974 Q107.033 539.363 104.696 537.256 Q102.358 535.15 98.353 535.15 Q96.478 535.15 94.603 535.567 Q92.7512 535.983 90.8067 536.863 L90.8067 519.502 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M60.4134 214.108 L68.0522 214.108 L68.0522 187.743 L59.7421 189.409 L59.7421 185.15 L68.0059 183.483 L72.6818 183.483 L72.6818 214.108 L80.3207 214.108 L80.3207 218.043 L60.4134 218.043 L60.4134 214.108 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M99.765 186.562 Q96.1539 186.562 94.3252 190.127 Q92.5197 193.669 92.5197 200.798 Q92.5197 207.905 94.3252 211.469 Q96.1539 215.011 99.765 215.011 Q103.399 215.011 105.205 211.469 Q107.033 207.905 107.033 200.798 Q107.033 193.669 105.205 190.127 Q103.399 186.562 99.765 186.562 M99.765 182.858 Q105.575 182.858 108.631 187.465 Q111.709 192.048 111.709 200.798 Q111.709 209.525 108.631 214.131 Q105.575 218.715 99.765 218.715 Q93.9549 218.715 90.8762 214.131 Q87.8206 209.525 87.8206 200.798 Q87.8206 192.048 90.8762 187.465 Q93.9549 182.858 99.765 182.858 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><polyline clip-path=\"url(#clip402)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"210.116,1445.72 211.448,1419.24 212.802,1399.56 216.667,1396.99 218.284,1413.94 218.435,1384.02 218.604,1419.99 219.485,1436.61 222.801,1411.48 223.04,1429.86 223.075,1366.33 227.704,1384.7 228.502,1352.12 232.663,1399.57 233.774,1397.42 235.93,1347.67 236.332,1390.12 239.914,1337.53 240.443,1357.11 240.781,1367.09 241.225,1328.75 241.429,1361.64 242.972,1362.92 244.14,1333.48 247.867,1340.29 250.016,1292.57 252.381,1327.43 254.259,1274.57 255.218,1327.36 262.735,1293.51 264.193,1281.87 264.702,1263.08 270.193,1291.5 270.321,1283.94 273.18,1231.56 273.288,1250.01 273.884,1267.49 275.506,1234.46 275.983,1247.02 277.568,1221.63 279.431
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"<path clip-path=\"url(#clip400)\" d=\"M221.211 198.898 L494.146 198.898 L494.146 95.2176 L221.211 95.2176 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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"<polyline clip-path=\"url(#clip400)\" style=\"stroke:#000000; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"221.211,198.898 494.146,198.898 494.146,95.2176 221.211,95.2176 221.211,198.898 \"/>\n",
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"<polyline clip-path=\"url(#clip400)\" style=\"stroke:#009af9; stroke-linecap:round; stroke-linejoin:round; stroke-width:4; stroke-opacity:1; fill:none\" points=\"245.711,147.058 392.715,147.058 \"/>\n",
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"<path clip-path=\"url(#clip400)\" d=\"M431.058 166.745 Q429.252 171.375 427.539 172.787 Q425.826 174.199 422.956 174.199 L419.553 174.199 L419.553 170.634 L422.053 170.634 Q423.812 170.634 424.784 169.8 Q425.757 168.967 426.937 165.865 L427.701 163.921 L417.215 138.412 L421.729 138.412 L429.831 158.689 L437.933 138.412 L442.446 138.412 L431.058 166.745 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip400)\" d=\"M449.738 160.402 L457.377 160.402 L457.377 134.037 L449.067 135.703 L449.067 131.444 L457.331 129.778 L462.007 129.778 L462.007 160.402 L469.645 160.402 L469.645 164.338 L449.738 164.338 L449.738 160.402 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
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]
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},
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|
"execution_count": 2,
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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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|
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|
"source": [
|
|
|
|
|
"x = sort(20 .* rand(1000) .- 10)\n",
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|
|
|
"y = (0.02 .* x .^ 3) .- x .+ 1 + rand(1000)\n",
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|
"\n",
|
|
|
|
|
"using Plots\n",
|
|
|
|
|
"# https://docs.juliaplots.org/latest/tutorial/\n",
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|
"\n",
|
|
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|
|
"plot(x, y)"
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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": 3,
|
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|
|
"id": "fafdd151-c5c4-494e-9793-60f45f49baff",
|
|
|
|
|
"metadata": {},
|
|
|
|
|
"outputs": [
|
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|
{
|
|
|
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|
"data": {
|
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|
|
"text/plain": [
|
|
|
|
|
"4-element Vector{Float64}:\n",
|
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|
|
|
" 0.020055886001898972\n",
|
|
|
|
|
" 8.201817529871014e-5\n",
|
|
|
|
|
" -1.001646828763499\n",
|
|
|
|
|
" 1.5016847772666466"
|
|
|
|
|
]
|
|
|
|
|
},
|
|
|
|
|
"execution_count": 3,
|
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|
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|
"metadata": {},
|
|
|
|
|
"output_type": "execute_result"
|
|
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|
|
}
|
|
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|
|
],
|
|
|
|
|
"source": [
|
|
|
|
|
"A = hcat(x.^3, x.^2, x, ones(1000));\n",
|
|
|
|
|
"coefficients = A \\ y"
|
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|
|
]
|
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|
|
},
|
|
|
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|
{
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
"execution_count": 4,
|
|
|
|
|
"id": "c01d514a-c7c0-4371-ac18-35cbed47d6c1",
|
|
|
|
|
"metadata": {},
|
|
|
|
|
"outputs": [
|
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|
|
{
|
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|
"data": {
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|
"image/png": "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"image/svg+xml": [
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"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n",
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"<defs>\n",
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" <clipPath id=\"clip440\">\n",
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" <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
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" </clipPath>\n",
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"</defs>\n",
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"<path clip-path=\"url(#clip440)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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"<defs>\n",
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" <clipPath id=\"clip441\">\n",
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" <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
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" </clipPath>\n",
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"</defs>\n",
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"<path clip-path=\"url(#clip440)\" d=\"M147.709 1486.45 L2352.76 1486.45 L2352.76 47.2441 L147.709 47.2441 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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"<defs>\n",
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" <clipPath id=\"clip442\">\n",
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]
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},
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"execution_count": 4,
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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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"plot(x, [y, A*coefficients])"
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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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"id": "427bb23c-0435-4c9c-8d45-6e912850c6d2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"3-element Vector{Float64}:\n",
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" -1.3463569041275599e-15\n",
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" 1.6972243622680054\n",
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" 5.302775637731994"
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]
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},
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"execution_count": 5,
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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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"A = [2 0 1;0 1 1; 0 0 0; 0 0 0];\n",
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"using LinearAlgebra # from stdlib\n",
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"\n",
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"eigvals(A' * A)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.9.3",
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"language": "julia",
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"name": "julia-1.9"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.9.3"
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}
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},
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"nbformat_minor": 5
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