I have a scaled PCA biplot (i.e. based on correlation matrix, not covariance matrix) of the first two PCs of a data set with 400 individuals and 26 variables (phenotypes).
The biplot indicates certain relationships between variables, based on the angles between the vectors. Some variables are positively correlated, others are negatively or not correlated at all. Why then, if I calculate and plot a Pearson's correlation between two columns in my data set, would the relationship be different from what's indicated on the biplot? (i.e. Pearson indicates a strong and significant negative correlation, but biplot shows vectors with an angle less than 90 degrees?)