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   "source": [
    "Chapter 04\n",
    "\n",
    "# 矩阵乘法操作\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": "d134e1be-222a-4fec-b5d9-78dfd4fcb3cc",
   "metadata": {},
   "source": [
    "该代码演示了 NumPy 中数组和矩阵的乘法操作，分别展示了逐元素乘法和矩阵乘法的不同结果。\n",
    "\n",
    "1. **逐元素乘法**：在第一个操作中，$A$ 和 $B$ 都是 `np.array` 类型。按逐元素方式进行乘法时，$A$ 将被广播到与 $B$ 形状相匹配，结果为：\n",
    "\n",
    "   $$\n",
    "   A \\odot B = \\begin{bmatrix} 1 \\times 5 & 2 \\times 6 \\\\ 1 \\times 8 & 2 \\times 9 \\end{bmatrix} = \\begin{bmatrix} 5 & 12 \\\\ 8 & 18 \\end{bmatrix}\n",
    "   $$\n",
    "\n",
    "2. **矩阵乘法**：在第二个操作中，$A$ 为 `np.array` 类型，而 $B$ 为 `np.matrix` 类型。此时 `*` 操作符按矩阵乘法执行，计算结果为：\n",
    "\n",
    "   $$\n",
    "   A \\times B = \\begin{bmatrix} 1 \\times 5 + 2 \\times 8 & 1 \\times 6 + 2 \\times 9 \\end{bmatrix} = \\begin{bmatrix} 21 & 24 \\end{bmatrix}\n",
    "   $$\n",
    "\n",
    "3. **矩阵乘法**：在第三个操作中，$A$ 和 $B$ 都是 `np.matrix` 类型，再次执行矩阵乘法，结果与第二个操作相同：\n",
    "\n",
    "   $$\n",
    "   A \\times B = \\begin{bmatrix} 21 & 24 \\end{bmatrix}\n",
    "   $$\n",
    "\n",
    "此代码展示了在 NumPy 中 `np.array` 和 `np.matrix` 类型的不同行为及 `*` 操作符在逐元素和矩阵乘法间的区别。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e694f73c-5da9-404b-930b-1b15c38c149e",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "04dd0c40-af12-47f6-8f60-1bba1b377b51",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dab05d3-2be2-47c9-97a5-e1b779132a1f",
   "metadata": {},
   "source": [
    "## 定义数组A和B并进行逐元素乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "87bb0d5c-67d8-4a10-95c8-c407a32932ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1, 2]])  # 定义数组A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8b9a1b34-090e-4432-a096-d45934e8c0aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.array([[5, 6],   # 定义数组B\n",
    "              [8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ef365f07-ebfe-432e-9ea3-bc45cecc0335",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5, 12],\n",
       "       [ 8, 18]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B # 打印A和B的逐元素乘法结果"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00486c88-927e-4c24-b2be-d6f9e8672e0f",
   "metadata": {},
   "source": [
    "## 定义数组A和矩阵B并进行矩阵乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "82d3c241-4790-40c4-aa1f-3a383250ba74",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1, 2]])  # 定义数组A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e6298ff4-cf44-4851-a835-d22563bd4d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.matrix([[5, 6],  # 定义矩阵B\n",
    "               [8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c036b953-8d3d-443e-87eb-1fe46fcd6014",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[21, 24]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B  # 打印A和B的矩阵乘法结果"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab903f71-3eb5-4290-a835-ae58622e69a4",
   "metadata": {},
   "source": [
    "## 定义矩阵A和矩阵B并进行矩阵乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ab60983c-0ad3-4263-ad82-84986df908d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.matrix([[1, 2]])  # 定义矩阵A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6ccade11-529f-4962-8eab-139e08a62592",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.matrix([[5, 6],   # 定义矩阵B\n",
    "               [8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e60a1889-600c-4982-9b61-3001d9fbd32f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[21, 24]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B  # 打印A和B的矩阵乘法结果"
   ]
  },
  {
   "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": []
  }
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