In this chapter, we introduce two related tools from linear algebra that have become true workhorses in countless areas of scientific computing: principal component analysis (PCA) and singular value decomposition (SVD). Essentially, we will talk about a decomposition 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 undergraduate linear algebra curricula, even though it is so widely used not only in geometric modeling and computer graphics, but also in computer vision, image processing, machine learning and many other applications.