Singular values and vectors underlie contemporary statistical data analysis. In particular, the method of principal component analysis (PCA) has assumed an ever increasing role in a wide range of applications, including machine learning, image processing, speech recognition, face recognition, data mining, semantics, and health informatics; see [94, 121, 122] and the references therein. The earliest descriptions of the method are to be found in the first half of the twentieth century in the work of the statisticians Karl Pearson, [184], and Harold Hotelling, [114].