拉格朗日乘子法和KKT条件
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转载自:http://www.cnblogs.com/zhangchaoyang/articles/2726873.html#3592012
拉格朗日乘子法(Lagrange Multiplier)和KKT(Karush-Kuhn-Tucker)条件是求解约束优化问题的重要方法,在有等式约束时使用拉格朗日乘子法,在有不等约束时使用KKT条件。前提是:只有当目标函数为凸函数时,使用这两种方法才保证求得的是最优解。
对于无约束最优化问题,有很多经典的求解方法,参见无约束最优化方法。
拉格朗日乘子法
先来看拉格朗日乘子法是什么,再讲为什么。
这个问题转换为
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0069.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/005B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/120/2211.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0031.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0069.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/005D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0031.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
其中
,称为拉格朗日乘子。
下面看一下wikipedia上是如何解释拉格朗日乘子法的合理性的。
现有一个二维的优化问题:
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0073.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0032.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
我们可以画图来辅助思考。
绿线标出的是约束
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
的等高线。箭头表示斜率,和等高线的法线平行。
从图上可以直观地看到在最优解处,f和g的法线方向刚好相反(或者说叫梯度共线),即
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/25BD.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/005B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/005D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BB.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
而满足
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0034.png?rev=2.6.1)
的解。
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/00A0.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BB.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0034.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
所以
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0034.png?rev=2.6.1)
等价。
新方程
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0046.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0079.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0063.png?rev=2.6.1)
总等于零。
KKT条件
先看KKT条件是什么,再讲为什么。
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0065.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0074.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size2/Regular/120/2211.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0031.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0071.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0035.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
其中
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/2264.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0036.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0037.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
上面的推导到此中断一下,我们看另外一个式子。
这里的
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0075.png?rev=2.6.1)
无关,所以这个等式就是成立的。
又
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size3/Regular/120/007B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/2212.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/221E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0064.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/006F.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0072.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/AMS/Regular/120/2234.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
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联合
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亦即
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我们把
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0038.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/007C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/060/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
。
最后总结一下:
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A7.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A9.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A8.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/007C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/060/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
KKT条件是拉格朗日乘子法的泛化,如果我们把等式约束和不等式约束一并纳入进来则表现为:
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A7.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A9.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23A8.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Size4/Regular/120/23AA.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BB.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0061.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006D.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/006E.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
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![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/004C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BB.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/002C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/03BC.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2202.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/007C.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/060/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/003D.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0030.png?rev=2.6.1)
注:
都是向量。
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0066.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0068.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/0069.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0067.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/085/006B.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0028.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Math/Italic/120/0078.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/085/2217.png?rev=2.6.1)
![](http://mathjax.cnblogs.com/2_6_1/fonts/HTML-CSS/TeX/png/Main/Regular/120/0029.png?rev=2.6.1)
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