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Covariance Matrix


Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by

 V_(ij)=cov(x_i,x_j)=<(x_i-mu_i)(x_j-mu_j)>,

where mu_i is the mean. Higher order matrices are given by

 V_(ij)^(mn)=<(x_i-mu_i)^m(x_j-mu_j)^n>.

An individual matrix element V_(ij)=cov(x_i,x_j) is called the covariance of x_i and x_j.


See also

Covariance, Error Propagation, Statistical Correlation, Variance

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References

Snedecor, G. W. and Cochran, W. G. Statistical Methods, 7th ed. Ames, IA: Iowa State Press, p. 342, 1980.

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Covariance Matrix

Cite this as:

Weisstein, Eric W. "Covariance Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CovarianceMatrix.html

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