文章目录
这里从《实用多元统计分析》(理查德~约翰逊)这本书里摘出一个例子,看题目:
- 引入相关模块
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/09bb4f3d269759ee2a25ae8ab1fb43166d22df3f.jpg)
- 创建几个符号,代码已知量
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/58af236d55fbb2fb595e96534c4a20a44623dc3f.jpg)
- sigma代表已知的X矩阵的协方差矩阵
sigma =
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/e6508eef76c6a7efbffe6767fefaaf51f2de665c.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/61183b2dd42a283403d3f84a58b5c9ea15cebf3f.jpg)
- u代表已知的x矩阵的均值向量
这是均值向量
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/99636c0e0cf3d7ca5e83f137f11fbe096b63a93f.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/5af4d7ea15ce36d3e8714d7139f33a87e950b13f.jpg)
- 、这是线性组合的系数矩阵
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/f15e24292df5e0fee4c046405f6034a85fdf725c.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/570f8c58d109b3de17672b29cfbf6c81810a4c5c.jpg)
- 计算均值向量,利用均值向量的计算公式:
代码为:
求得:
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/9304c888d43f8794105b866fd11b0ef41ad53a88.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/1b0d4f0fd9f9d72a5311de5cd72a2834349bbb3f.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/cdfe7281800a19d82ddb4b4430fa828ba71e465c.jpg)
同样,我们利用协方差矩阵的公式:
代码为:求得结果为:
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/b29f8282d158ccbfe14b7b7b1ad8bc3eb03541b9.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/e1bf8725bc315c60b44da4ae8eb1cb134854775c.jpg)
![python 线性代数:[16]线性组合均值协方差阵](/2016/02/03/python%20%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%EF%BC%9A%5B16%5D%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88%E5%9D%87%E5%80%BC%E5%8D%8F%E6%96%B9%E5%B7%AE%E9%98%B5/b13fd48065380cd7dc6b6caca244ad345982813f.jpg)
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