Book4_Power-of-Matrix/Book4_Ch02_Python_Codes/Bk4_Ch02_02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 02\n",
    "\n",
    "# L2范数\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab88dee3-1a2e-4357-b6b5-136abf3073c5",
   "metadata": {},
   "source": [
    "此代码定义了两个二维列向量 `a` 和 `b`，并计算它们的L2范数。L2范数也称为欧几里得范数，用于测量向量的长度。公式如下：\n",
    "\n",
    "$$\n",
    "\\| a \\|_2 = \\sqrt{a_1^2 + a_2^2}\n",
    "$$ \n",
    "\n",
    "对于向量 `a` 和 `b`，L2范数分别为：\n",
    "\n",
    "$$\n",
    "\\| a \\|_2 = \\sqrt{4^2 + 3^2} = 5\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\| b \\|_2 = \\sqrt{(-3)^2 + 4^2} = 5\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a36cd49-a4e6-4321-a7e8-7f9a34c6aaef",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "01a128eb-3998-4172-bd8a-ec95a23bbc83",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ad8b4b0-856b-47a7-adb8-b020180d0c30",
   "metadata": {},
   "source": [
    "## 定义两个列向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "212d3a51-f2c6-4785-8c9a-40fa93ae0566",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4],\n",
       "       [3]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[4], [3]])  # 定义向量a，值为[4, 3]\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8d5f6350-fddc-4633-946e-f21797b6f5e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3],\n",
       "       [ 4]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[-3], [4]])  # 定义向量b，值为[-3, 4]\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3ba8142-26a8-43d6-b777-685207499ca9",
   "metadata": {},
   "source": [
    "## 计算L2范数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1954434f-cb3e-44d3-b985-45b73af8a815",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_L2_norm = np.linalg.norm(a)  # 计算向量a的L2范数\n",
    "a_L2_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8110a0d6-c941-4825-bf60-bc989324f592",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_L2_norm = np.linalg.norm(b)  # 计算向量b的L2范数\n",
    "b_L2_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}