* I need (properties + Therom ) about correlation matrix ( write the references from which the information was taken ple

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I Need Properties Therom About Correlation Matrix Write The References From Which The Information Was Taken Ple 1 (33.94 KiB) Viewed 21 times

* I need (properties + Therom ) about correlation matrix ( write the references from which the information was taken please) Correlation and Covariance Matrix For a random vector X, we define the correlation matrix, Rx, as X;X;X; ... XX1 EXEXXz1 ... EX X.]] Xxx EX- XEIXŞI EļX-XI Rx = E[XX")= E (xXX.X: EX.X:1 EX.X:) ... EXI where shows matrix transposition The covariance matrix, Cx, is defined as Cx = E[OX - EXHX - EX)" X; - EX (X; - EX XX; - EX) ... X-EXXX. - EX.) (X: - EX:)(x1 - EX:) X: - EX (X; - EXOX. - EX.) X. - EX. 1x. - EX.XX1 - Exi) (X. - EX.XX; - EX) Varcx) CovX, X:) CoveX. X.) CovcX. X) Var(X) CovX, X.) Cov(XX) CovX.X2) Varcx.) The covariance matrix is a generalization of the variance of a random variable. Remember that for a random variable, we have Var(x) = EX? - (EX). The following example extends this formula to random vectors.