1. For the notion in quantum mechanics, see scattering matrix.

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.

Definition

Given n samples of m, the sample mean is

is the j.

The scatter matrix is the m-by-m positive semi-definite matrix

denotes matrix transpose, and multiplication is with regards to the outer product. The scatter matrix may be expressed more succinctly as

is the n-by-n centering matrix.

Application

The maximum likelihood estimate, given n samples, for the covariance matrix of a multivariate normal distribution can be expressed as the normalized scatter matrix

has a Wishart distribution.

See also

• Estimation of covariance matrices

• Sample covariance matrix

• Wishart distribution

• Outer productor X⊗X is the outer product of X with itself.

• Gram matrix

References