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AI数学打卡第3天|特征值与特征向量 Python

  • 2026-08-18 23:11:25
AI数学打卡第3天|特征值与特征向量 Python

AI数学打卡第3天｜特征值与特征向量 Python

AI数学打卡第3天｜特征值与特征向量 Python完整实操笔记

做深度学习、大模型的人都绕不开特征值和特征向量，它是PCA降维、Embedding向量分解、模型特征提取的底层核心数学工具，今天打卡线性代数重点章节，把理论+代码一次性梳理清楚。

先理清核心基础定义：对于方阵A，满足Ax=\lambda x的\lambda就是特征值，对应的向量x为特征向量。简单理解，矩阵变换中只拉伸、不改变方向的向量就是特征向量，拉伸倍数就是特征值。

很多人只会死记公式，不会落地，这份笔记配套完整Python代码，依靠numpy库一键求解矩阵特征值与特征向量，不用手动计算繁琐行列式，零基础也能跑通。

同时结合AI场景拆解用途：图像处理降维依靠特征分解简化像素矩阵；大模型Embedding做特征筛选时，会通过特征值大小区分有效信息与噪声；推荐系统的协同过滤矩阵，底层同样依赖这套运算逻辑。

学习顺序先吃透理论推导，再逐行运行代码验证结果，对比手动计算与程序输出，快速吃透抽象概念。打卡式分段学习降低入门门槛，每天搞定一个线性代数核心模块，循序渐进补齐AI必备数学短板。


#AI数学基础
#线性代数学习
#特征值特征向量
#深度学习数学
#Python数学代码
#机器学习入门
#AI自学打卡
#大模型底层知识
#数学实操干货
#数据分析基础

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  139. /yingpanguazai/ssd/ssd1/www/f.mffb.com.cn/runtime/temp/067d451b9a0c665040f3f1bdd3293d68.php ( 11.98 KB )
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  1. CONNECT:[ UseTime:0.000949s ] mysql:host=127.0.0.1;port=3306;dbname=f_mffb;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.001479s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.006574s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000712s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.001474s ]
  6. SELECT * FROM `set` [ RunTime:0.000634s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.001562s ]
  8. SELECT * FROM `article` WHERE `id` = 507377 LIMIT 1 [ RunTime:0.001514s ]
  9. UPDATE `article` SET `lasttime` = 1787341477 WHERE `id` = 507377 [ RunTime:0.003317s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 66 LIMIT 1 [ RunTime:0.000620s ]
  11. SELECT * FROM `article` WHERE `id` < 507377 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.001270s ]
  12. SELECT * FROM `article` WHERE `id` > 507377 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.001174s ]
  13. SELECT * FROM `article` WHERE `id` < 507377 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.002161s ]
  14. SELECT * FROM `article` WHERE `id` < 507377 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.001778s ]
  15. SELECT * FROM `article` WHERE `id` < 507377 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.002925s ]
0.192158s