协方差矩阵的几何意义A geometric interpretation of the covariance matrix

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协方差矩阵定义了数据的形状;对角线是方差,非对角线是协方差

Two-dimensional normally distributed data is explained completely by its mean and its 2\times 2 covariance matrix(二维正态分布数据通过其均值和协方差矩阵得到了完全解释)

covariance matrix defines the shape of the data. Diagonal spread is captured by the covariance, while axis-aligned spread is captured by the variance.

the covariance matrix defines both the spread (variance), and the orientation (covariance) of our data.(描述了数据的分布和方向)