COURSE TOPICS:

Chapter 1: Linear Equations and Matrices
1.1 Systems of Linear Equations
1.2 Matrices
1.3 Matrix Multiplication
1.4 Algebraic Properties of Matrix Operations
1.5 Special Types of Matrices and Partitioned Matrices
1.6 Matrix Transformations
1.7 Computer Graphics
1.8 Correlation Coefficient

Chapter 2: Solving Linear Systems
2.1 Echelon Form of a Matrix
2.2 Elementary Matrices: Finding A$^{-1}$
2.3 Equivalent Matrices
2.4 LU-Factorization

Chapter 3: Real Vector Spaces
3.1 Vectors in the Plane and in 3-space
3.2 Vector Spaces
3.3 Subspaces
3.4 Span and Linear Dependence
3.5 Basis and Dimension
3.6 Homogeneous Systems
3.7 Coordinates and Isomorphisms
3.8 Rank of a Matrix

Chapter 4: Inner Product Spaces
4.1 Length and Direction in R^2 and R^3
4.3 Inner Product Spaces
4.4 Gram-Schmidt Process
4.5 Orthogonal Complements
4.6 Least Squares

Chapter 5: Linear Transformations and Matrices
5.1 Definition and Examples
5.2 Kernel and Range of a Linear Transformation
5.3 Matrix of a Linear Transformation
5.5 Similarity

Chapter 6: Determinants
6.1 Definition
6.2 Properties of Determinants
6.3 Cofactor Expansion
6.4 Inverse of a Matrix

Chapter 7: Eigenvalues and Eigenvectors
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization and Similar Matrices
7.3 Markov Processes
7.4 Diagonalization of Symmetric Matrices
7.5 Spectral Decomposition and Singular Value Decomposition

(This schedule is subject to change.)