Chapter 1: Systems of Linear Equations
            1.1 Solving Systems of Linear Equations
            1.2 Vectors and Matrices
            1.3 Kernels, Rank, Homogeneous Equations

Chapter 2: Vector Spaces and Transformations
            2.1 Euclidean Vector Spaces
            2.2 Lines, Planes, and Hyperplanes
            2.3 Linear Transformations
            2.4 General Vector Spaces

Chapter 3: Matrix Operations
            3.1 Matrices
            3.2 Matrix Inverses

Chapter 4: Determinants
            4.1 Determinants: Introduction
            4.2 Determinants: Properties

Chapter 5: Vector Spaces
            5.1 Column, Row, and Null Spaces
            5.2 Bases and Dimension
            5.3 Coördinate Systems

Chapter 6: Eigensystems
            6.1 Eigenvalues and Eigenvectors

Chapter 7: Inner Product Vector Spaces
            7.1 Inner Product Spaces
            7.2 Orthogonality

Chapter 8: Additional Topics
            8.1 Hermitian Matrices and Spectral Thm.
            8.2 Matrix Factorizations and Block Matrices
            8.3 Iterative Methods for Linear Equations