DSPA Chapter 4 Linear Algebra and Matrix Computing

Linear algebra is a branch of mathematics that studies linear associations using vectors, vector-spaces, linear equations, linear transformations and matrices. Although it is generally challenging to visualize complex data, e.g., large vectors, tensors, and tables in n-dimensional Euclidean spaces, linear algebra allows us to represent, model, synthesize and summarize such compex data.

In this chapter, we review the fundamentals of linear algebra, matrix manipulation and their applications to representation, modeling, and analysis of real data. Specifically, we will cover (1) construction of matrices and matrix operations, (2) general matrix algebra notations, (3) eigenvalues and eigenvectors of linear operators, (4) least squares estimation, and (5) linear regression and variance-covariance matrices.