DSPA Chapter 4 Linear Algebra and Matrix ComputingLinear 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.