LIST OF TOPICS
The following is a list of topics that will be covered in
this course along with the chapter and section numbers. The chapter and section numbers
are taken from the textbook "Linear Algebra"
(3rd Edition), by J. Fraleigh and R. Beauregard. There may also be several concepts presented
that are not in the book.
CHAPTER 1. VECTORS, MATRICES, AND LINEAR SYSTEMS
1.1 Vectors in Euclidean Spaces
1.2 The Norm and the Dot Product
1.3 Matrices amd their Algebra
1.4 Solving Systems of Linear Equations
1.5 Inverses of Square Matrices
1.6 Homogeneous Systems, Subspaces, and Bases
CHAPTER 2. DIMENSION, RANK, AND LINEAR TRANSFORMATIONS
2.1 Independence and Dimension
2.2 The Rank of a Matrix
2.3 Linear Transformations of Euclidean Spaces
2.4 Linear Transformations of the Plane
CHAPTER 3. VECTOR SPACES
3.1 Vector Spaces
3.2 Basic Concepts of Vector Spaces
CHAPTER 4. DETERMINANTS
4.1 Areas, Volumes, and Cross Products
4.2 The Determinant of a Square Matrix
4.3 Computation of Determinants and Cramer's Rule
CHAPTER 5. EIGENVALUES AND EIGENVECTORS
5.1 Eigenvalues and Eigenvectors
5.2 Diagonalization
CHAPTER 6. ORTHOGONALITY
6.1 Projections
6.2 The GramSchmidt Process
6.3 Orthogonal Matrices
6.5 The Method of Least Squares
