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Correlation Matrix

The correlation matrix of random variables X_1,...,X_d having positive standard deviations sigma_1,...,sigma_d is the matrix R with entries

R_(ij)=(cov(X_i,X_j))/(sigma_isigma_j).

It is the standardized covariance matrix. Every correlation matrix is real symmetric, positive semidefinite, and has unit diagonal. Conversely, every real symmetric positive semidefinite matrix with unit diagonal is a correlation matrix.

See also

Correlation Coefficient, Covariance Matrix, Positive Semidefinite Matrix, Random Variable

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References

Mardia, K. V.; Kent, J. T.; and Bibby, J. M. Multivariate Analysis. London, England: Academic Press, 1979.

Cite this as:

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

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