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   "source": [
    "Chapter 04\n",
    "\n",
    "# 矩阵逆\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": "c83af894-1177-41f1-9e0c-5df36a5e4755",
   "metadata": {},
   "source": [
    "该代码演示了 `np.matrix` 和 `np.array` 在计算矩阵逆时的区别。矩阵 $A$ 被定义为 `np.matrix` 类型，直接使用 `.I` 属性即可求逆；而矩阵 $B$ 被定义为 `np.array` 类型，不支持 `.I` 属性，因此会报错。\n",
    "\n",
    "矩阵 $A$ 的定义为：\n",
    "\n",
    "$$\n",
    "A = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "其逆矩阵为：\n",
    "\n",
    "$$\n",
    "A^{-1} = \\begin{bmatrix} -2 & 1 \\\\ 1.5 & -0.5 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "`np.matrix` 类型允许直接调用 `.I` 属性计算逆矩阵，而 `np.array` 类型则需使用 `numpy.linalg.inv` 函数求逆。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7654b39-8ea4-480f-9b62-949c3e52bbfe",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e3ba8f7c-9319-46f3-a52c-9eeef1ed5ae5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b11501ac-e96b-45ab-9563-63977efe46f7",
   "metadata": {},
   "source": [
    "## 定义矩阵A并计算其逆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "368c1708-7217-4844-9b32-3e9398c15358",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.matrix([[1, 2],  # 定义为np.matrix类型的矩阵A\n",
    "               [3, 4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "56017ddb-fe6d-4d98-ba7a-963a3b854428",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.   1. ]\n",
      " [ 1.5 -0.5]]\n"
     ]
    }
   ],
   "source": [
    "print(A.I)  # 打印矩阵A的逆矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb72cfe6-f62d-42a2-ac12-3a551854f4cb",
   "metadata": {},
   "source": [
    "## 定义数组B并尝试计算其逆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "abc5a48d-5499-41e4-b826-a9b63acfd8ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.array([[1, 2],  # 定义为np.array类型的数组B\n",
    "              [3, 4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "afd919b3-7d56-4543-b1fb-a78bca4bbc26",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'numpy.ndarray' object has no attribute 'I'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[6], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28mprint\u001b[39m(B\u001b[38;5;241m.\u001b[39mI)\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'I'"
     ]
    }
   ],
   "source": [
    "print(B.I)  # 尝试打印数组B的逆，会报错"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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