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

I. T. Jolliffe, Principal Component Analysis, 2nd ed., New York: Springer, 2004.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed., New York: Springer, 2009.