# canonical correlation to calculate the strong correlation between 2 groups of variables

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.