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Correlation - Correlation matrices | | Correlation - Correlation matrices: Encyclopedia II - Correlation - 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. Consequent ...
See also:Correlation, Correlation - Pearson's product-moment coefficient, Correlation - Mathematical properties, Correlation - The sample correlation, Correlation - Non-parametric correlation coefficients, Correlation - Other measures of dependence among random variables, Correlation - Copulas and correlation, Correlation - Correlation matrices, Correlation - Correlation does not imply causation | | | Correlation, Correlation - Copulas and correlation, Correlation - Correlation does not imply causation, Correlation - Correlation matrices, Correlation - Mathematical properties, Correlation - Non-parametric correlation coefficients, Correlation - Other measures of dependence among random variables, Correlation - Pearson's product-moment coefficient, Correlation - The sample correlation | | |
| | | Correlation: Encyclopedia II - Correlation - Correlation matrices
Correlation - 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.
The correlation matrix is symmetrical (the correlation between Xi and Xj is the same as the correlation between Xj and Xi).
Other related archivesCauchy-Schwarz inequality, Francis Galton, Non-parametric, Pearson product-moment correlation coefficient, Spearman's ρ, absolute value, acausal, copula, correlation implies causation (logical fallacy), correlation ratio, covariance, covariance matrix, cross-correlation, cumulative distribution functions, dimensions, electron correlation, equation, expected values, functions, independent, jointly normal, linear dependence, linear submanifold, means, multivariate normal distribution, mutual information, non-negative definite matrix, normally distributed, parametric statistic, probability theory, random variables, spurious relationship, standard deviations, statistics
 Adapted from the Wikipedia article "Correlation matrices", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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