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The Covariance Matrix
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In this video we define the covariance matrix of a random vector. We show that this matrix encodes the variance of any linear combination of the random vector, and also the variance of the vector in any direction. We then explain how to compute the sample covariance matrix from a dataset, where each data point consists of multiple features. Finally, we show that the sample variance encodes the sample variance of any linear combination of the features, and also the sample variance of the data in any direction.
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