aa转置的秩为什么等于A的秩
【aa转置的秩为什么等于A的秩】在矩阵理论中，矩阵的秩是一个非常重要的概念，它反映了矩阵所代表的线性变换的“信息量”或“自由度”。对于一个矩阵 $ A $，其转置矩阵为 $ A^T $，而 $ A A^T $ 是一个方阵。在很多数学问题中，我们经常需要了解 $ A A^T $ 的秩与原矩阵 $ A $ 的秩之间的关系。本文将从理论和实例两个角度来解释 为什么 $ text{rank}(A A^T) = text{rank}(A) $。
1到100的序数词
【1到100的序数词】在日常生活中，我们经常需要用到序数词来表示顺序或排名。例如，“第一”、“第二”、“第三”等。掌握从1到100的序数词，不仅有助于语言表达的准确性，还能提升学习和工作的效率。以下是对1到100序数词的总结与整理。
一、序数词的基本规则
序数词通常由基数词加“-th”构成，但有一些例外情况需要特别注意：
- 1 → first
- 2 → second
- 3 → third
- 5 → fifth
- 8 → eighth
- 9 → ninth
- 12 → twelfth
- 20 → twentieth
- 30 → thirtieth
- 40 → fortieth
- 50 → fiftieth
- 60 → sixtieth
- 70 → seventieth
- 80 → eightieth
- 90 → ninetieth
其他数字则基本遵循“基数词 + th”的结构，如“fourth”（第四）、“seventh”（第七）等。
二、1到100的序数词表
| 序号 | 基数词 | 序数词 |
| 1 | one | first |
| 2 | two | second |
| 3 | three | third |
| 4 | four | fourth |
| 5 | five | fifth |
| 6 | six | sixth |
| 7 | seven | seventh |
| 8 | eight | eighth |
| 9 | nine | ninth |
| 10 | ten | tenth |
| 11 | eleven | eleventh |
| 12 | twelve | twelfth |
| 13 | thirteen | thirteenth |
| 14 | fourteen | fourteenth |
| 15 | fifteen | fifteenth |
| 16 | sixteen | sixteenth |
| 17 | seventeen | seventeenth |
| 18 | eighteen | eighteenth |
| 19 | nineteen | nineteenth |
| 20 | twenty | twentieth |
| 21 | twenty-one | twenty-first |
| 22 | twenty-two | twenty-second |
| 23 | twenty-three | twenty-third |
| 24 | twenty-four | twenty-fourth |
| 25 | twenty-five | twenty-fifth |
| 26 | twenty-six | twenty-sixth |
| 27 | twenty-seven | twenty-seventh |
| 28 | twenty-eight | twenty-eighth |
| 29 | twenty-nine | twenty-ninth |
| 30 | thirty | thirtieth |
| 31 | thirty-one | thirty-first |
| 32 | thirty-two | thirty-second |
| 33 | thirty-three | thirty-third |
| 34 | thirty-four | thirty-fourth |
| 35 | thirty-five | thirty-fifth |
| 36 | thirty-six | thirty-sixth |
| 37 | thirty-seven | thirty-seventh |
| 38 | thirty-eight | thirty-eighth |
| 39 | thirty-nine | thirty-ninth |
| 40 | forty | fortieth |
| 41 | forty-one | forty-first |
| 42 | forty-two | forty-second |
| 43 | forty-three | forty-third |
| 44 | forty-four | forty-fourth |
| 45 | forty-five | forty-fifth |
| 46 | forty-six | forty-sixth |
| 47 | forty-seven | forty-seventh |
| 48 | forty-eight | forty-eighth |
| 49 | forty-nine | forty-ninth |
| 50 | fifty | fiftieth |
| 51 | fifty-one | fifty-first |
| 52 | fifty-two | fifty-second |
| 53 | fifty-three | fifty-third |
| 54 | fifty-four | fifty-fourth |
| 55 | fifty-five | fifty-fifth |
| 56 | fifty-six | fifty-sixth |
| 57 | fifty-seven | fifty-seventh |
| 58 | fifty-eight | fifty-eighth |
| 59 | fifty-nine | fifty-ninth |
| 60 | sixty | sixtieth |
| 61 | sixty-one | sixty-first |
| 62 | sixty-two | sixty-second |
| 63 | sixty-three | sixty-third |
| 64 | sixty-four | sixty-fourth |
| 65 | sixty-five | sixty-fifth |
| 66 | sixty-six | sixty-sixth |
| 67 | sixty-seven | sixty-seventh |
| 68 | sixty-eight | sixty-eighth |
| 69 | sixty-nine | sixty-ninth |
| 70 | seventy | seventieth |
| 71 | seventy-one | seventy-first |
| 72 | seventy-two | seventy-second |
| 73 | seventy-three | seventy-third |
| 74 | seventy-four | seventy-fourth |
| 75 | seventy-five | seventy-fifth |
| 76 | seventy-six | seventy-sixth |
| 77 | seventy-seven | seventy-seventh |
| 78 | seventy-eight | seventy-eighth |
| 79 | seventy-nine | seventy-ninth |
| 80 | eighty | eightieth |
| 81 | eighty-one | eighty-first |
| 82 | eighty-two | eighty-second |
| 83 | eighty-three | eighty-third |
| 84 | eighty-four | eighty-fourth |
| 85 | eighty-five | eighty-fifth |
| 86 | eighty-six | eighty-sixth |
| 87 | eighty-seven | eighty-seventh |
| 88 | eighty-eight | eighty-eighth |
| 89 | eighty-nine | eighty-ninth |
| 90 | ninety | ninetieth |
| 91 | ninety-one | ninety-first |
| 92 | ninety-two | ninety-second |
| 93 | ninety-three | ninety-third |
| 94 | ninety-four | ninety-fourth |
| 95 | ninety-five | ninety-fifth |
| 96 | ninety-six | ninety-sixth |
| 97 | ninety-seven | ninety-seventh |
| 98 | ninety-eight | ninety-eighth |
| 99 | ninety-nine | ninety-ninth |
| 100 | hundred | hundredth |
三、使用建议
在实际应用中，序数词常用于：
- 排名：如“第一名”、“第三名”
- 时间顺序：如“第十五天”、“第二十次”
- 日期表达：如“1月1日”写作“January 1st”
- 文本编号：如“第3章”、“第12节”
掌握这些序数词，可以更准确地进行书面和口头表达，避免误解和错误。
通过以上总结与表格，你可以快速查阅并掌握1到100的序数词，为学习英语或日常交流提供有力支持。
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1到100的序数词