A friend or mine has performed a PCA and he asked me for help about interpretating a biplot.
In that biplot I found that the vector representing a variable, say A, forms a very wide angle, perhaps around 120º, with those of the rest of variables (say B and C). Furthermore, it has negative loadings for PC2. I interpreted this as PC2 separating individuals with high values of B and C and low values of A from individuals with high values of A and low values of B and C.
In addition, I thought that angles between variables, represented as vectors in biplot, were related with original variables correlations. So I thought A would be slightly but negatively correlated with both B and C because of the angle their vectors form.
But correlation matrix for A, B and C shows positive correlations in all cases. Is this possible? Should be interpreted angles between variables in biplot in some other way because we have constructed new reference axes (now our reference axes are PCs)?
Edit: I think it is not the same question as this one; this question is about particular values of angles in biplot, not about general interpretation of biplots; thanks @amoeba for editing the title.