Correlation matrix

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} $.