Book4_Power-of-Matrix/Book4_Ch10_Python_Codes/Bk4_Ch10_01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 10\n",
    "\n",
    "# 数据正交投影\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": "23cd38cd-efb3-4836-81ea-9043eee65da6",
   "metadata": {},
   "source": [
    "这段代码从 `sklearn` 的 `load_iris` 数据集中提取了鸢尾花数据，计算其 Gram 矩阵和特征向量，并通过一系列矩阵操作和热图可视化了数据与特征向量的关系。具体步骤如下：\n",
    "\n",
    "1. **Gram 矩阵计算**：首先定义了四个特征：萼片长度 \\( x_1 \\)、萼片宽度 \\( x_2 \\)、花瓣长度 \\( x_3 \\) 和花瓣宽度 \\( x_4 \\)，将原始数据矩阵 \\( X \\) 计算为矩阵的列。然后计算 Gram 矩阵 \\( G = X^T X \\) 和其特征值与特征向量：\n",
    "\n",
    "   $$\n",
    "   G = X^T X\n",
    "   $$\n",
    "\n",
    "   其中，\\( G \\) 为 \\( 4 \\times 4 \\) 的对称矩阵，表示数据的相似度。\n",
    "\n",
    "2. **特征向量的矩阵操作**：对于每个特征向量 \\( v_j \\)，定义以下几组计算：\n",
    "\n",
    "   - **组 1**：将 \\( X \\) 投影到 \\( v_j \\) 上得到 \\( z_j \\)，即：\n",
    "   \n",
    "     $$\n",
    "     z_j = X v_j\n",
    "     $$\n",
    "   \n",
    "     通过热图展示 \\( X \\)、\\( v_j \\) 和 \\( z_j \\) 的结果。\n",
    "\n",
    "   - **组 2**：使用 \\( z_j \\) 和 \\( v_j^T \\) 的乘积重建矩阵 \\( X_j \\)，即：\n",
    "   \n",
    "     $$\n",
    "     X_j = z_j v_j^T\n",
    "     $$\n",
    "   \n",
    "     展示 \\( z_j \\)、\\( v_j^T \\) 和 \\( X_j \\) 的结构。\n",
    "\n",
    "   - **组 3**：构造矩阵 \\( T_j \\) 为 \\( v_j v_j^T \\)，这是一个投影矩阵，使任何向量在 \\( v_j \\) 上投影，满足 \\( T_j T_j = T_j \\) 的幂等性：\n",
    "\n",
    "     $$\n",
    "     T_j = v_j v_j^T\n",
    "     $$\n",
    "\n",
    "   - **组 4**：计算 \\( X T_j \\) 用于近似原始数据矩阵 \\( X \\) 中与 \\( v_j \\) 对应的部分：\n",
    "\n",
    "     $$\n",
    "     X_j = X T_j\n",
    "     $$\n",
    "\n",
    "3. **可视化**：通过 `seaborn` 绘制热图展示原始矩阵和计算过程中的中间矩阵，使矩阵乘法和特征向量投影的过程更直观可见。这种可视化方法帮助展示数据和特征向量之间的关系，以及 Gram 矩阵的正交基的构成和投影。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29baf153-c8f4-41f3-8d7c-1dc0e96d8b4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns  # 导入数据可视化库\n",
    "import numpy as np  # 导入数值计算库\n",
    "import matplotlib.pyplot as plt  # 导入绘图库\n",
    "import pandas as pd  # 导入数据处理库\n",
    "from sklearn.datasets import load_iris  # 导入鸢尾花数据集加载器"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca8aaa4f-9031-464c-9edd-2f3c6398b485",
   "metadata": {},
   "source": [
    "## 加载数据并定义特征名称"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "99dc5f8a-0d29-4b10-ac40-da9109162750",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a247144e-b675-4522-8e8a-cebe5db1324c",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eea5b1a3-4438-49c3-98dd-c930855eed40",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "71c7e6e1-6e48-4483-844e-bb4990ece919",
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = ['Sepal length, x1', 'Sepal width, x2', 'Petal length, x3', 'Petal width, x4']\n",
    "X_df = pd.DataFrame(X, columns=feature_names)  # 将 X 转换为数据框"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13acec3e-02db-483e-a39e-2f508c7ffc8f",
   "metadata": {},
   "source": [
    "## 提取数据和计算 Gram 矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "832d3c4f-c3fd-4fc0-bde8-c9f1b8dcfc5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X_df.to_numpy()  # 将数据框转换为数组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "144b0f7b-9f67-4646-ac5a-e5389360cee2",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = X.T @ X  # 计算 Gram 矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ecea30ff-724d-4a11-a9cc-7d2e8ddf0e10",
   "metadata": {},
   "outputs": [],
   "source": [
    "D, V = np.linalg.eig(G)  # 计算特征值和特征向量"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2f0d594-50f3-40c4-bbaa-e2e4459c6afe",
   "metadata": {},
   "source": [
    "## 定义函数：绘制热图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6faae63d-6d93-4614-bd88-741e783b8020",
   "metadata": {},
   "outputs": [],
   "source": [
    "def heatmap(Matrices, Titles, Ranges, Equal_tags):\n",
    "    M1, M2, M3 = Matrices  # 提取矩阵\n",
    "    Title_1, Title_2, Title_3 = Titles  # 提取标题\n",
    "    \n",
    "    fig, axs = plt.subplots(1, 5, figsize=(12, 3))  # 创建子图\n",
    "    \n",
    "    plt.sca(axs[0])\n",
    "    ax = sns.heatmap(M1, cmap='RdYlBu_r', vmin=Ranges[0][0], vmax=Ranges[0][1],\n",
    "                     cbar=False, xticklabels=False, yticklabels=False)\n",
    "    if Equal_tags[0]:\n",
    "        ax.set_aspect(\"equal\")\n",
    "    plt.title(Title_1)\n",
    "    \n",
    "    plt.sca(axs[1])\n",
    "    plt.title('=')\n",
    "    plt.axis('off')\n",
    "    \n",
    "    plt.sca(axs[2])\n",
    "    ax = sns.heatmap(M2, cmap='RdYlBu_r', vmin=Ranges[1][0], vmax=Ranges[1][1],\n",
    "                     cbar=False, xticklabels=False, yticklabels=False)\n",
    "    if Equal_tags[1]:\n",
    "        ax.set_aspect(\"equal\")\n",
    "    plt.title(Title_2)\n",
    "    \n",
    "    plt.sca(axs[3])\n",
    "    plt.title('@')\n",
    "    plt.axis('off')\n",
    "    \n",
    "    plt.sca(axs[4])\n",
    "    ax = sns.heatmap(M3, cmap='RdYlBu_r', vmin=Ranges[2][0], vmax=Ranges[2][1],\n",
    "                     cbar=False, xticklabels=False, yticklabels=False)\n",
    "    if Equal_tags[2]:\n",
    "        ax.set_aspect(\"equal\")\n",
    "    plt.title(Title_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37e9c69d-0e86-4c66-b1cc-69587eb17495",
   "metadata": {},
   "source": [
    "## 定义函数：绘制四组图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6a8dd604-782f-4594-ac6e-d23c7c1917cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_four_figs(X, v_j, idx):\n",
    "    z_j = X @ v_j  # 计算投影 z_j\n",
    "    Titles = ['$X$', '$v_' + str(idx) + '$', '$z_' + str(idx) + '$']\n",
    "    Ranges = [[-2, 11], [-1, 1], [-2, 11]]\n",
    "    Equal_tags = [False, True, False]\n",
    "    heatmap([X, v_j, z_j], Titles, Ranges, Equal_tags)  # 绘制第一个图形组\n",
    "\n",
    "    X_j = z_j @ v_j.T  # 计算 X_j\n",
    "    Titles = ['$z_' + str(idx) + '$', '$v_' + str(idx) + '^T$', '$X_' + str(idx) + '$']\n",
    "    heatmap([z_j, v_j.T, X_j], Titles, Ranges, Equal_tags)  # 绘制第二个图形组\n",
    "\n",
    "    T_j = v_j @ v_j.T  # 计算 T_j\n",
    "    Titles = ['$v_' + str(idx) + '$', '$v_' + str(idx) + '^T$', '$T_' + str(idx) + '$']\n",
    "    Ranges = [[-1, 1], [-1, 1], [-1, 1]]\n",
    "    Equal_tags = [True, True, True]\n",
    "    heatmap([v_j, v_j.T, T_j], Titles, Ranges, Equal_tags)  # 绘制第三个图形组\n",
    "\n",
    "    T_j = X @ T_j  # 计算 X @ T_j\n",
    "    Titles = ['$X$', '$T_' + str(idx) + '$', '$X_' + str(idx) + '$']\n",
    "    Ranges = [[-2, 11], [-1, 1], [-2, 11]]\n",
    "    Equal_tags = [False, True, False]\n",
    "    heatmap([X, T_j, X_j], Titles, Ranges, Equal_tags)  # 绘制第四个图形组"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "267c4166-760c-4997-bd78-c12caf25dd59",
   "metadata": {},
   "source": [
    "## 绘制四个特征向量的图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e82cce96-cb42-40d3-928e-a4980f008d0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJ1lUqlUnoEAAAA1eNEEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgmf8F9ZjeJ1gbdLsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = V[:, 0].reshape((-1, 1))\n",
    "plot_four_figs(X, v1, 1)  # 第一个基向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c99bc669-7cfb-453f-82c1-53dd2b87c98b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v2 = V[:, 1].reshape((-1, 1))\n",
    "plot_four_figs(X, v2, 2)  # 第二个基向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "90d32098-7fc6-4334-aa24-e55fb98584d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v3 = V[:, 2].reshape((-1, 1))\n",
    "plot_four_figs(X, v3, 3)  # 第三个基向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a4e23db9-f3c4-4078-b3bc-1e5bf9c3512c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4IAAAEPCAYAAAAXuHpOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAQG0lEQVR4nO3dXYjcd73H8W8m261ux01Po3kwKmljI2LMxppuotGVWixqQAopAcspiW1FL7TEQbsnwRKQsARN1QXBLCq0c6EpFVPwoqCimLYmWDbBbFLaxbiBeOFT1k07IdU2O+eiOLCndROO2flt5/t6wUL///ldfG5y8e5/HhY0m81mAAAAkEal9AAAAADaSwgCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEACnv55ZejXq/H5s2bY8mSJdHV1RVLly6N2267Ler1ely8eLH0RKDDLGg2m83SIwAAshobG4utW7fGn//85/jMZz4T69evj7e//e1x7ty5OHLkSNTr9XjLW94SjzzySKxatar0XKBDFA/BzZs3x7PPPhunTp2acb/ZbEZ/f390d3fHU089VWgdAMDcOXnyZHzwgx+MO++8M/bt2xfXXHPNq85cuHAhvvSlL8Xjjz8ev/nNb2LFihUFlgKdpvhbQ9etWxcTExPRaDRm3K/X6zE6OhrDw8OFlkH7NJvNePnlly/rD4DOcPHixdi6dWvcc8898d3vfvc1I7DZbEZ3d3fs378/PvKRj8TnP//5AkuBTlQ8BPv6+qLZbMbJkydb986fPx+7du2Kbdu2xfr161v3Dx8+HJVKJfbs2VNiKsyZX//613HVVVdd1t/p06dLzwXgCjhw4ECcP38+9u7dGxER09PT8bWvfS1WrFgRb3zjG2PLli2xb9++uPXWWyMi4lvf+lb84he/iN///vclZwMdoqv0gL6+voh45f3xGzZsiIiIvXv3xvPPPx9DQ0Otc9PT07Fjx47o7+8vshPm0vvf//54+umnL+vsW9/61jleA0A7PPbYY7F9+/bo7u6OiIjvfOc78fWvfz2Ghobive99bxw8eDAeeOCB2LhxY0RELF68OD7wgQ/Er371q3jnO99ZcjrQAYqH4I033hg9PT0xNjYWERFnzpyJBx98MB544IFYvnx569zIyEhs2rQpJicnS02FOVOtVmPdunWXdbarq/g/WwCugPHx8fj0pz/duh4ZGYmdO3fGfffdFxERt9xyS5w4cSKmp6dbZ5YuXRp//etf274V6DzF3xpaqVRizZo1rRAcHByMZcuWRa1Wa505e/ZsDA8Px+7du0vNhDnlraEA+bz00kvxhje8oXU9MTERN91004wzN99884zrP/7xj/HmN7+5LfuAzjYvHi309fXFwYMH48iRI3HgwIF49NFH4+qrr269vnPnzqjVarFo0aKCK2HueGsoQD7veMc7Ynx8PD75yU9GxCtP+/7v/+ybmJho/ff4+Hj89re/jYcffridM4EONW9C8Hvf+17cfffdMTAwEFu2bGm9Njo6GkePHo39+/cXXAhz601vetOML0YCoPPddtttceDAgdixY0dERGzdujWGhoZizZo1sXbt2vjpT38aBw8ejI0bN8bPf/7z+NznPhdf+MIX4oYbbig7HOgIxX9HMCLiySefjA9/+MNRqVRidHR0xmelvv3tb8euXbuip6cnIiIajUYsXLgwtmzZEvV6vdBiAID/zNTUVKxatSq++c1vxrZt26LRaMRdd90Vjz32WES88j0Kt99+e3zjG9+IpUuXxle+8pWo1WqxYMGCssOBjjAvQnA2jUYjpqamWte1Wi1WrlwZg4ODsXjx4nLDAAD+Qz/+8Y/jrrvuiocffji2bt0aERF/+ctfYnJyMt71rnfF3//+95iamorrr79eAAJX1Lx4a+hsqtVqVKvV1nVPT0/09vaKQADgde+OO+6IF198MbZv3x71ej0++9nPRn9/f6xcuTL+9Kc/tT4T+MILL8TPfvYzMQhcMfP+iSAAQKebmJiIoaGh+MlPfjLjp7KWL18ed955Z9x///2xZMmSgguBTiMEAQDmienp6Thz5kycO3currvuunjb295WehLQoYQgAABAMsV/UB4AAID2EoIAAADJCEEAAIBkLvvnI6YPfXkud8wblYF9pScAAADMKU8EAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAANrm9OnTsWDBgsv6e+6550rP7VhdpQcAAAB5XHfddXH48OHWdaPRiI997GNx++23x+Dg4Iyzq1evbve8NIQgAADQNr29vbFx48bW9VNPPRUREbfeeuuM+8wtbw0FAACKOXr0aERE3HTTTYWX5CIEAQCAYo4dOxaVSiX6+vpKT0lFCAIAAMUcO3YsVq9eHddcc82/PXP48OGoVCqxZ8+eNi7rbEIQAAAo4p///GecPHly1reFTk9Px44dO6K/v7+NyzqfL4sBAACKOHHiRLz00kuzhuDIyEhs2rQpJicn27is83kiCAAAFHHs2LGI+PdfFHP27NkYHh6O3bt3t3NWCkIQAAAo4l/fGPq+973vNV/fuXNn1Gq1WLRoUTtnpSAEAQCAIo4dOxbXX399XHvtta96bXR0NI4ePRr33ntv+4cl4DOCAABA201PT8fx48fj4x//+Gu+/sQTT8QzzzwTS5YsiYiIRqMRCxcujPHx8ajX6+2c2pEWNJvN5uUcnD705bneMi9UBvaVngAAAOk1Go2YmppqXddqtVi5cmUMDg7G4sWLyw3rEJ4IAgAA8061Wo1qtdq67unpid7eXhF4hQhBAABg3nvooYdKT+goviwGAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACS8a2hAABwBTWnflR6wqzO9WwoPeGSXrzYW3rCrJae/n7pCbNa8O7/ueQZTwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQTNflHnxy1Vfncse8MVB6AAAAwBzzRBAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAMxLP/jBD6JarUa1Wo3u7u646qqrWtcf/ehHS88DgNc1IQjAvHTPPfdEo9GIRqMR27dvjy9+8Yut61/+8pel5wHA65oQBGDeO378eKxdu7b0DADoGF2lBwDAbJrNZpw4cUIIAq8b53o2lJ4wq2svPF16wiU1L7xQesKsnl12X+kJs3r3ZZzxRBCAee3UqVPxj3/8I97znveUngIAHUMIAjCv/e53v4vVq1fH1VdfXXoKAHQMIQhA223evDlWrVr1qvvNZjNuvvnm2LRpU+uezwcCwJUnBAFou3Xr1sXExEQ0Go0Z9+v1eoyOjsbw8HDrnhAEgCtPCALQdn19fdFsNuPkyZOte+fPn49du3bFtm3bYv369a37QhAArjzfGgpA2/X19UVExNjYWGzY8Mq36+3duzeef/75GBoamnH21KlTbd8HAJ3OE0EA2u7GG2+Mnp6eGBsbi4iIM2fOxIMPPhi7du2K5cuXzzh7+PDhqFQqsWfPnhJTAaAjCUEA2q5SqcSaNWtaITg4OBjLli2LWq0249z09HTs2LEj+vv7S8wEgI7lraEAFNHX1xcHDx6MI0eOxIEDB+LRRx991U9EjIyMxKZNm2JycrLQSgDoTJ4IAlBEX19f/O1vf4u77747BgYGYsuWLTNeP3v2bAwPD8fu3bsLLQSAzuWJIABF/OsLY5577rn44Q9/+KrXd+7cGbVaLRYtWtTuaQDQ8YQgAEV86EMfimaz+ZqvjY6OxtGjR2P//v1tXgUAOQhBAOadJ554Ip555plYsmRJREQ0Go1YuHBhjI+PR71eL7wOAF7/hCAA8869994bd9xxR+u6VqvFypUrY3BwsOAqAOgcQhCAeadarUa1Wm1d9/T0RG9vbyxevLjgKgDoHEIQgHnvoYceKj0BADqKn48AAABIRggCAAAkIwQBAACS8RlBgDkyfejLpSfM6slVXy09YVZjZ6ZKT5jVJ+7/VOkJs7rh0PHSEwCYxzwRBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMl0Xe7BsTNTczhj/hhYcW3pCQAAvI69eLG39IRZNS+8UHrCpZ2bLL1gVn/ovlB6wqze/V89lzzjiSAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQTFfpAQCdqjKwr/SEWQ2UHnAJAyuuLT1hdoeOl14AAP9vnggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyXSVHgAAAJ1k6envl54wq2eX3Vd6wiX9oftC6QmzumXkv0tPmN3exy95xBNBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMl0Xe7BT9z/qbncMX8cOl56AQAAwJzyRBAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJLGg2m83LOfiHgbVzvWVeuOHQ8dITAAAA5pQnggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJCEEAAIBkhCAAAEAyQhAAACAZIQgAAJCMEAQAAEhGCAIAACQjBAEAAJIRggAAAMkIQQAAgGSEIAAAQDJCEAAAIBkhCAAAkIwQBAAASEYIAgAAJCMEAQAAkhGCAAAAyQhBAACAZBY0m81m6REAAAC0jyeCAAAAyQhBAACAZIQgAABAMkIQAAAgGSEIAACQjBAEAABIRggCAAAkIwQBAACSEYIAAADJ/C+kTSkxPmwXzQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v4 = V[:, 3].reshape((-1, 1))\n",
    "plot_four_figs(X, v4, 4)  # 第四个基向量"
   ]
  },
  {
   "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
}