The construction of principal components is illustrated. This Demonstration considers the case for two variables and that are simulated as multivariate normal with zero means, unit variances, and theoretical correlation . The sample size can be 10, 100, or 999, and there are three graphs.
Graph 1: the data is plotted along with the Karhunen–Loeve directions
Graph 2: the data is shown projected on each of the two Karhunen–Loeve directions; note that there are data points
Graph 3: the principal components are plotted corresponding to each direction; visually, the principal components are the coordinates of the projected points in each of the directions