# Correlation matrix

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The matrix of correlation coefficients of several random variables. If $X _ {1} \dots X _ {n}$ are random variables with non-zero variances $\sigma _ {1} ^ {2} \dots \sigma _ {n} ^ {2}$, then the matrix entries $\rho _ {ij}$( $i \neq j$) are equal to the correlation coefficients (cf. Correlation coefficient) $\rho ( X _ {i} , X _ {j} )$; for $i = j$ the element is defined to be 1. The properties of the correlation matrix ${\mathsf P}$ are determined by the properties of the covariance matrix $\Sigma$, by virtue of the relation $\Sigma = B {\mathsf P} B$, where $B$ is the diagonal matrix with (diagonal) entries $\sigma _ {1} \dots \sigma _ {n}$.

How to Cite This Entry:
Correlation matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Correlation_matrix&oldid=46526
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article