# how to check if makes sense to do canonical correlation?

I wanted to check if it is reasonable to do a canonical correlation analysis on my covariance matrix. I am trying to follow Wichern's book:

The author says that we have to test if $$\sum_{12}=0$$.

Here is my first question: I have my values for my $$\sum_{12}$$ which is a 3x2 matrix with none of the values being 0 (isn't this enough?)

(I guess not), because then the author continues with:

What does the likelihood ratio means here? and what is the test about, I do have the values of the matrix $$\sum_{12}$$

I am not an expert in stats, I get a bit lost with all the formulas, a practical example in R would be great: I just want to learn how to check if it's worth doing a canonical correlation analysis. (note that I am only working with the covariance matrix)