{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 04\n",
    "\n",
    "# 转置\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": "34fd7eb5-f8ae-40eb-832c-23f93d07cfeb",
   "metadata": {},
   "source": [
    "该代码定义了一个 $3 \\times 2$ 矩阵 $A$，并计算其转置矩阵。矩阵 $A$ 定义为：\n",
    "\n",
    "$$\n",
    "A = \\begin{bmatrix} 1 & 2 \\\\ 3 & 4 \\\\ 5 & 6 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "矩阵的转置 $A^T$ 将行变为列，结果为一个 $2 \\times 3$ 的矩阵：\n",
    "\n",
    "$$\n",
    "A^T = \\begin{bmatrix} 1 & 3 & 5 \\\\ 2 & 4 & 6 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "代码使用了两种方法来计算转置矩阵：`A.transpose()` 方法和 `A.T` 属性，二者等效。这段代码展示了如何在 NumPy 中对矩阵进行转置操作。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4562dc5f-106d-458a-9c21-058f45dc7750",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "492fc116-d1e3-404a-92fc-92bf126234a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58efb734-2fce-475e-a954-2ff78a1bf71f",
   "metadata": {},
   "source": [
    "## 定义矩阵A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1581437b-c937-42fc-b1f1-c176a48b0a33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2],  # 定义矩阵A\n",
    "              [3, 4],\n",
    "              [5, 6]])\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13eeb291-b311-4823-a983-c9749695b2e2",
   "metadata": {},
   "source": [
    "## 计算矩阵的转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d34daecc-75e6-4f6f-9af7-d506d9d73eb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 5],\n",
       "       [2, 4, 6]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_T = A.transpose()  # 使用transpose方法计算A的转置\n",
    "A_T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5ac7a53b-8e59-40ee-a2d8-dafe251f386d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 5],\n",
       "       [2, 4, 6]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_T_2 = A.T  # 使用.T属性计算A的转置\n",
    "A_T_2"
   ]
  },
  {
   "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": []
  }
 ],
 "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
}