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