
Chapter 4
PCA and SVD
Olga Sorkine-Hornung
In this chapter, we introduce two related tools from linear alge-
bra that have become true workhorses in countless areas of scien-
tific computing: principal component analysis (PCA) and singular
value decomposition (SVD). Essentially, we will talk about a de-
composition of a given matrix into several factors that are easy to
analyze and reveal important properties of the matrix and hence
the data, or the problem in which the matrix arises. Surprisingly,
the singular value decomposition is often excluded from under-
graduate linear algebra curricula, even though it is so widely used
not only in geometric modeling ...