Sample Covariance
The sample covariance matrix is a K-by-K matrix with entries
where is an estimate of the covariance between the jth variable and the kth variable of the population underlying the data. In terms of the observation vectors, the sample covariance is
Alternatively, arranging the observation vectors as the columns of a matrix, so that
- ,
which is a matrix of K rows and N columns. Here, the sample covariance matrix can be computed as
- ,
where is an N by 1 vector of ones. If the observations are arranged as rows instead of columns, so is now a 1×K row vector and is an N×K matrix whose column j is the vector of N observations on variable j, then applying transposes in the appropriate places yields
Read more about this topic: Sample Mean And Sample Covariance
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