Matrix Theory From Eigenvalues to Data Insights

In linear algebra, the Singular Value Decomposition (SVD) of a matrix is a factorization of that matrix into three matrices. It has some interesting algebraic properties and conveys important geometrical and theoretical insights about linear transformations. It also has some important applications in data science. In this chapter, we will try to explain the mathematical intuition behind SVD and its geometrical meaning. We will use SageMath libraries to do the calculations instead of manual calculations, and later give you some examples of using SVD in data science applications.

In this article, bold-face lower-case letters (like \(\mathbf{a}\)) refer to vectors. Bold-face capital letters (like \(\mathbf{A}\)) refer to matrices, and italic lower-case letters (like \(a\)) refer to scalars.