A Geometric Depiction Of Covariance

Nikolai Janakiev explains the concept of the covariance matrix using a bit of Python and some graphs:

In this article we saw the relationship of the covariance matrix with linear transformation which is an important building block for understanding and using PCASVD, the Bayes Classifier, the Mahalanobis distance and other topics in statistics and pattern recognition. I found the covariance matrix to be a helpful cornerstone in the understanding of the many concepts and methods in pattern recognition and statistics.

Many of the matrix identities can be found in The Matrix Cookbook. The relationship between SVD, PCA and the covariance matrix are elegantly shown in this question.

Understanding covariance is critical for a number of statistical techniques, and this is a good way of describing it.

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