Chapter 5. Linear Algebra
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
