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   "source": [
    "Chapter 04\n",
    "\n",
    "# 矩阵乘法\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": "f78179ac-736d-417f-964f-a079c966931d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "该代码定义了两个 $2 \\times 2$ 的矩阵 $A$ 和 $B$，并计算了它们的矩阵乘积。矩阵 $A$ 和 $B$ 分别为：\n",
    "\n",
    "$$\n",
    "A = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 2 & 4 \\\\ 1 & 3 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "矩阵乘积 $A @ B$ 的计算结果为：\n",
    "\n",
    "$$\n",
    "A @ B = \\begin{bmatrix} 1 \\cdot 2 + 2 \\cdot 1 & 1 \\cdot 4 + 2 \\cdot 3 \\\\ 3 \\cdot 2 + 4 \\cdot 1 & 3 \\cdot 4 + 4 \\cdot 3 \\end{bmatrix} = \\begin{bmatrix} 4 & 10 \\\\ 10 & 24 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "代码中，矩阵乘法操作使用了 `np.matmul` 函数和 `@` 运算符两种方式。这展示了 NumPy 中进行矩阵乘法的两种等效方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc4e525d-60d4-4447-a29e-2e1ead9aa96e",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "80885172-f546-4973-add9-496ddb779de5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bef4a295-b3fe-493c-9baf-04b2a95d913e",
   "metadata": {},
   "source": [
    "## 定义两个矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8abe8f8d-6398-4bb6-ac14-a1b1139873fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2],  # 定义矩阵A\n",
    "              [3, 4]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dbb8337a-f940-4337-9a98-65692ff3e854",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 4],\n",
       "       [1, 3]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([[2, 4],  # 定义矩阵B\n",
    "              [1, 3]])\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd37527e-b082-4899-a2fe-6b04c8db9fea",
   "metadata": {},
   "source": [
    "## 矩阵乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "313d8fec-6e35-4e36-900f-efa4bd5c6adc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4, 10],\n",
       "       [10, 24]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_times_B = np.matmul(A, B)  # 使用np.matmul计算矩阵A和B的乘积\n",
    "A_times_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3efab8d4-012b-4f28-b515-d9047d180a89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4, 10],\n",
       "       [10, 24]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_times_B_2 = A @ B  # 使用@操作符计算矩阵A和B的乘积\n",
    "A_times_B_2"
   ]
  },
  {
   "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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