I feel like the case of bivariate PCA is pretty uncommon. The classic example of PCA is over large numbers of variables that have been transformed to be short-tailed and have similar variance (or which just had similar/​small variance to begin with before any transformations). Under that condition, PCA gives you the dimensions which correlate with as many variables as possible.
I feel like the case of bivariate PCA is pretty uncommon. The classic example of PCA is over large numbers of variables that have been transformed to be short-tailed and have similar variance (or which just had similar/​small variance to begin with before any transformations). Under that condition, PCA gives you the dimensions which correlate with as many variables as possible.