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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:

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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)

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