My question is related to the computation of correlation coefficient of a block covariance matrix. The correlation coefficient can be computed as:

r = cov(X,Y)/std(X) std(Y)

But if I have a block covariance matrix A=[CXX  CXY ;CYX CYY ] (where C is R2 and A is R4)and I want to calculate the correlation coefficient, can I use the above formula or is there any other method for its calculation?

The ultimate aim is to choose CXY in such a way that we get maximum correlation. (A should remain positive semi definite).

Please help

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