Correlation

::This article is about the correlation coefficient between two random variables. The term correlation can also mean the cross-correlation of two functions or electron correlation in molecular systems.

Correlation matrices

The correlation matrix of n random variables X1, ..., Xn is the n  ×  n matrix whose i,j entry is corr(Xi, Xj). If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables Xi /SD(Xi) for i = 1, ..., n. Consequently it is necessarily a non-negative definite matrix.

Related Topics:
Covariance matrix - Non-negative definite matrix

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The correlation matrix is symmetrical (the correlation between X_i and X_j is the same as the correlation between X_j and X_i).

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