In principal component analysis and related techniques, we approximate (in the least squares sense) as n x m matrix F by an n x m matrix G which satisfies rank(G) ≤ p, where p < min(n,m). Or equivalenty, we want to find an n x p matrix X and an m x p matrix Y such that G = XY' approximates F as closely as possible. The rows of X and Y are then often used in graphical displays. In particular, biplots represent X and Y jointly as n + m points in Euclidean p space.