Book4_Power-of-Matrix/Book4_Ch04_Python_Codes/Bk4_Ch04_15.ipynb

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    "Chapter 04\n",
    "\n",
    "# 行列式\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "该代码定义了一个 $2 \\times 2$ 矩阵 $A$，并计算其行列式。矩阵 $A$ 的定义为：\n",
    "\n",
    "$$\n",
    "A = \\begin{bmatrix} 4 & 2 \\\\ 1 & 3 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "行列式计算公式为：\n",
    "\n",
    "$$\n",
    "\\det(A) = A_{11} A_{22} - A_{12} A_{21}\n",
    "$$\n",
    "\n",
    "具体计算得：\n",
    "\n",
    "$$\n",
    "\\det(A) = 4 \\cdot 3 - 2 \\cdot 1 = 12 - 2 = 10\n",
    "$$\n",
    "\n",
    "该代码使用 `np.linalg.det` 函数来计算行列式的值。"
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   "cell_type": "markdown",
   "id": "38e823dc-d626-4fba-8ac6-3fc7d73e9486",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
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   "execution_count": 1,
   "id": "1c1d325e-6981-4885-a9c1-d59bdbe0a194",
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   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd7164de-4737-4076-89d3-3f7b8e5b988b",
   "metadata": {},
   "source": [
    "## 定义矩阵A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "194dc241-67d8-4ca1-a752-e6c7d2237c94",
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   "source": [
    "A = np.array([[4, 2],  # 定义矩阵A\n",
    "              [1, 3]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bf849ff-6000-4d22-8e57-8d15debbb248",
   "metadata": {},
   "source": [
    "## 计算矩阵A的行列式"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d910437e-4d72-4c09-8618-a809968077a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "det_A = np.linalg.det(A)  # 计算矩阵A的行列式"
   ]
  },
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   "execution_count": null,
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