I have three data vectors $A$, $B$ and $C$ that are all more or less correlated.
What I want is a meaningful definition for a measure of the degree of correlation between those parts of $A$ and $B$ that are not correlated with $C$.
I do apologize if this is not fully understandable. I struggle to come to an easier formulation of the problem. However I can give an example:
Example: Say $A$, $B$, $C$ could all be binary, i.e. only contain the values 0 and 1. I then would want to know the number of positions where $A$ and $B$ are 1 and $C$ is 0.
As a side note: How does one "uncorrelate" variables, i.e. given two variables $A$ and $B$ how to split $A$ into a part that is maximally correlated with B and another that is maximally uncorrelated?