In multivariate statistics and probability theory, the scatter matrix is a statistic that is used to make estimates of the covariance matrix, for instance of the multivariate normal distribution.
Given n samples of m-dimensional data, represented as the m-by-n matrix,
denotes matrix transpose,[2] and multiplication is with regards to the outer product.
The scatter matrix may be expressed more succinctly as where
The maximum likelihood estimate, given n samples, for the covariance matrix of a multivariate normal distribution can be expressed as the normalized scatter matrix When the columns of
are independently sampled from a multivariate normal distribution, then
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