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I am new to canonical correlation and I was trying to understand canonical correlation to calculate the strong correlation between 2 groups of variables. I could use the method on matlab. But I am having hard time to understand to solve it manually. Let’s say, Group 1 variables are ( $X_1$, $X_2$) group 2 variables are ($X_3$, $X_4$ ) 4 different variables.

Normal distributions with covariance = “6/7” and a variance of each =1.

The variance-covariance matrix:

$ \Sigma =\begin{bmatrix} 1 & 6/7 & 6/7 & 6/7 \\ 6/7 & 1 & 6/7 & 6/7 \\ 6/7 & 6/7 & 1 & 6/7 \\ 6/7 & 6/7 & 6/7 & 1 \end{bmatrix}$

How can I find the strongest possible effect of variables $X_1$ , $X_2$ on variables $X_3$ , $X_4$ and separately the lowest possible effect. How can I Accomplish this part by finding specific two linear combinations of $X_1$ ,$X_2$ along with specific two linear combination of $X_3$ , $X_4$ . How can I calculate numerical values of coefficients for those linear combinations. Also how can I find numerical values of corresponding correlations.

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