Cross-correlation matrix: Difference between revisions

Revision as of 18:16, 28 December 2018

Revision as of 19:29, 29 December 2018

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==Uncorrelatedness==

Two random vectors <math>\mathbf{X}=(X_1,...\ldots,X_m)^{\rm T} </math> and <math>\mathbf{Y}=(Y_1,...\ldots,Y_n)^{\rm T} </math> are called '''uncorrelated''' if

:<math>\operatorname{E}[\mathbf{X} \mathbf{Y}^{\rm T}] = \operatorname{E}[\mathbf{X}]\operatorname{E}[\mathbf{Y}]^{\rm T}.</math>.

They are uncorrelated if and only if their covariance <math>\operatorname{K}_{\mathbf{X}\mathbf{Y}}</math> matrix is zero.

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:<math>\operatorname{E}[\mathbf{Z} \mathbf{W}^{\rm H}] = \operatorname{E}[\mathbf{Z}]\operatorname{E}[\mathbf{W}]^{\rm H}</math>

and

:<math>\operatorname{E}[\mathbf{Z} \mathbf{W}^{\rm T}] = \operatorname{E}[\mathbf{Z}]\operatorname{E}[\mathbf{W}]^{\rm T}.</math>.

==Properties==