Linear algebra has been described as the mathematics of computer science, and this chapter will be a bit different from prior chapters. Prior chapters discussed topics such as regression and statistical significance tests, and techniques that can directly be applied to a dataset to produce a solution of interest. A single linear algebra technique in isolation rarely provides a solution of interest to a substantive researcher. However, many numerical analysis techniques rely on linear algebra and matrix operations, making them an important part of scientific computing.
In this chapter, we will discuss the following topics:
Matrix properties
Mathematical operations on matrices
Matrix inversion
Solving linear systems
Eigenvalues and eigenvectors
LU decomposition
Singular value decomposition of a matrix
Choleski decomposition of a matrix
Outer products
Applications of linear algebra using R