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For random variables ''X''(''s'') and ''X''(''t'') at different points ''s'' and ''t'' of some space, the correlation function is
:<math>C(s,t) = \operatorname{corr} ( X(s), X(t) )
where <math>\operatorname{corr}</math> is described in the article on [[correlation]]. In this definition, it has been assumed that the stochastic variable is scalar-valued. If it is not, then more complicated correlation functions can be defined. For example, if ''X''(''s'') is a vector, then a matrix of correlation functions is defined as
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