complete_numpy_course_for_beginners.ipynb

{
 "cells": [
  {
   "attachments": {
    "numpy_logo.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "56758853",
   "metadata": {},
   "source": [
    "<div style=\"text-align:center\">\n",
    "        <h1>\n",
    "            Complete NumPy course for beginners\n",
    "        </h1>\n",
    "</div>\n",
    "\n",
    "<br><br>\n",
    "\n",
    "![numpy_logo.png](attachment:numpy_logo.png)\n",
    "\n",
    "\n",
    "<br><br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4eefd941",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from sklearn.datasets import load_sample_image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0122d25f",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8846b8f8",
   "metadata": {},
   "source": [
    "### Array basics (ndarray class)\n",
    "\n",
    "<table style=\"width:75%\">\n",
    "\n",
    "  <tr style=\"background-color: transparent\">\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/1d_array.png\" width=\"200\"/>\n",
    "    </td>\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/2d_array.png\" width=\"200\"/>\n",
    "    </td>\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/3d_array.png\" width=\"250\"/>\n",
    "    </td>\n",
    "\n",
    "  </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "190127df",
   "metadata": {},
   "source": [
    "<table style=\"width:75%\">\n",
    "\n",
    "  <tr style=\"background-color: transparent\">\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/txt_array.png\" width=\"200\"/>\n",
    "    </td>\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/bool_array.png\" width=\"200\"/>\n",
    "    </td>\n",
    "    <td valign=\"bottom\">\n",
    "        <img src=\"images/obj_array.png\" width=\"200\"/>\n",
    "    </td>\n",
    "\n",
    "  </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "345db300",
   "metadata": {},
   "source": [
    "###### Data types:\n",
    "\n",
    "- **Float**: np.float16, np.float32, np.float64\n",
    "\n",
    "\n",
    "- **Integer**: np.int8, np.int16, np.int32, np.int64, np.uint8, np.uint16, np.uint32, np.uint64\n",
    "\n",
    "\n",
    "- **Complex**: np.complex64, np.complex128\n",
    "\n",
    "\n",
    "- **Boolean**: np.bool\n",
    "\n",
    "\n",
    "- **String**: np.str\n",
    "\n",
    "\n",
    "- **Object**: np.object\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92e05335",
   "metadata": {},
   "source": [
    "###### Advantages of NumPy n-dimensional arrays vs Python collections\n",
    "\n",
    "\n",
    "- Implemented in C\n",
    "\n",
    "\n",
    "- Memory efficiency\n",
    "\n",
    "\n",
    "- Flexibility\n",
    "\n",
    "\n",
    "- Vectorized operations\n",
    "\n",
    "\n",
    "- Processing speed"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88c00242",
   "metadata": {},
   "source": [
    "### Why numpy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bae4cbc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_python(n):\n",
    "    a = [i for i in range(n)]\n",
    "    b = [i for i in range(n)]\n",
    "    c = [None] * n\n",
    "    start = time.perf_counter()\n",
    "    for i in range(n):\n",
    "        c[i] = a[i] + b[i]\n",
    "    end = time.perf_counter()\n",
    "    return end - start\n",
    "\n",
    "def sum_numpy(n):\n",
    "    a = np.arange(n)\n",
    "    b = np.arange(n)\n",
    "    start = time.perf_counter()\n",
    "    c = a + b\n",
    "    end = time.perf_counter()\n",
    "    return end - start\n",
    "\n",
    "experiments = [100, 1000, 10000, 1000000]\n",
    "python_results = [sum_python(n) for n in experiments]\n",
    "numpy_results = [sum_numpy(n) for n in experiments]\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.xlabel(\"Array size\", size=14)\n",
    "plt.ylabel(\"Execution time\", size=14)\n",
    "plt.title(\"Execution time in seconds\", size=18)\n",
    "sns.lineplot(x=experiments, y=python_results, color='r', label='Python list')\n",
    "sns.lineplot(x=experiments, y=numpy_results, color='b', label='NumPy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1803deee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cdcf8880",
   "metadata": {},
   "source": [
    "###### Array properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d2b5304",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62451fc5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eb436713",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "7e9676bd",
   "metadata": {},
   "source": [
    "### Indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f61c65e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78cf999f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "236c71b6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "294b1e5d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c73502a7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e0d5f50e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "067100e8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72610d40",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2716e9b6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "5834caa4",
   "metadata": {},
   "source": [
    "### Copying and editing arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bfb85fed",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c0c4296",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "22665feb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab9073c6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ec4cc5ff",
   "metadata": {},
   "source": [
    "### Reshaping and stacking arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba584643",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "459913da",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f942f6ef",
   "metadata": {},
   "source": [
    "###### Stacking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d04bd8f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7445d93",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "129359ae",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c32983c6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "05cfd1fe",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "846b7951",
   "metadata": {},
   "source": [
    "###### Adding new axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b389d1cb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9168b5ce",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95cef45c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7cd5d2d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "83368244",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "de5eb5f6",
   "metadata": {},
   "source": [
    "###### Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b72462c0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e872c95",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "887fb383",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6015ee56",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f0e1cfdb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea874155",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9ec8d501",
   "metadata": {},
   "source": [
    "### Arithmetic operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0fd32799",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5738c026",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "832d4ab0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a88173df",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa225438",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f8afb22",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c3f039d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4b06f96",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "538b7ea0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54653221",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca27dcbf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3c0a272f",
   "metadata": {},
   "source": [
    "### Applying a mathematical formula: $f(x) = \\frac {1} {\\sigma \\sqrt{2\\pi}} e^{-\\frac {1}{2} \\left(\\frac {x - \\mu} {\\sigma}\\right)^2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce5a77b9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "a170a1df",
   "metadata": {},
   "source": [
    "### Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "674c645e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c44971c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dfdac7b9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d36128b6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f15fb5ef",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98627577",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "357d7432",
   "metadata": {},
   "source": [
    "### Basic operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f2f4241d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2cad696c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48ac5e0d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b625f8e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4eb1f503",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97bd1593",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fe5b9996",
   "metadata": {},
   "source": [
    "###### Concatenate arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7e2a4ac",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a726b6be",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f2df279f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fef11a21",
   "metadata": {},
   "source": [
    "###### Flip arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24397e7b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f1543de",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3c31962",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3aef8448",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "63a8f071",
   "metadata": {},
   "source": [
    "### Saving and loading numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0e86d18",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b163e8a1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee9dd7e6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7c323a1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81fa5d8e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "aa85c846",
   "metadata": {},
   "source": [
    "### Random numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "277ef0d2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d89732e9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3989891b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a9827ad",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12a8ade9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5f2d1bc6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6b28e7e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcc1f9d8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a029ecbf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4346a873",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c02cfa7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "0d519b4b",
   "metadata": {},
   "source": [
    "### Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73d7964e",
   "metadata": {},
   "source": [
    "###### Chi-square samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b87f6ae8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50710237",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c7e1c285",
   "metadata": {},
   "source": [
    "###### Poisson samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35b24733",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3db6eb3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ef5f3874",
   "metadata": {},
   "source": [
    "###### Normal samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f280eff",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e635409",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b17f2d66",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "952bc710",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d7b2f9bd",
   "metadata": {},
   "source": [
    "### Linear algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2acc4ab8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "13c5a3ec",
   "metadata": {},
   "source": [
    "###### Transpose matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e87550ee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e18dc9e4",
   "metadata": {},
   "source": [
    "###### Trace of a matrix:  $\\text{Tr}(M)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02a38585",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "7eb85b66",
   "metadata": {},
   "source": [
    "###### Determinant of a matrix: $\\det(M)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b91994d6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "496ca989",
   "metadata": {},
   "source": [
    "###### Inverse of a matrix: $M^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d1daba2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "aad3f368",
   "metadata": {},
   "source": [
    "###### Matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "68fc4a61",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8475373",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "23544ab9",
   "metadata": {},
   "source": [
    "###### Inner product of two vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f30a3f2c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "9a2062b0",
   "metadata": {},
   "source": [
    "###### Eigendecomposition of a matrix: $A = Q\\Lambda Q^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "75317a8b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b677338",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af979d90",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e7070029",
   "metadata": {},
   "source": [
    "###### Single value decomposition (SVD)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0cdf4ee6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "40463c4c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea0c01f8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "505088ce",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3591ac6a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee922dc6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0784d021",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "00a589bb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3a7006a4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d464ef3e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd3ec914",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eaf5315c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ce4b669",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db261511",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c458aee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6a177ce",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31d9d80a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1e2a4a3c",
   "metadata": {},
   "source": [
    "### Trigonometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "34e3ed63",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "30445e41",
   "metadata": {},
   "source": [
    "###### Sine function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "517b08f2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "46981a9d",
   "metadata": {},
   "source": [
    "###### Cosine function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4622fe8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "0e448959",
   "metadata": {},
   "source": [
    "###### Hyperbolic functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c684ee62",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e128c293",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b7c21c95",
   "metadata": {},
   "source": [
    "### Plotting the Julia set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5d90dfc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af1adcb0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37b95ef3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8df6c2e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0bbeba98",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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