I have past data which is in vector form. The information shows the probabilities of a AAA rated company to migrate to another credit rating. So for example, (x1, x2, x3) has the probabilities of moving from AAA to AAA, AA or A.

If I take the correlation matrix between all these vectors, and so I end up with a 3x3 matrix, what is the interpretation of the resulting matrix?

Furthermore, what does it mean to take a correlation matrix associated with an initial rating state


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