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- Lecture 1: Vectors and Vector Spaces
- Lecture 2: The Geometry of Vectors
- Lecture 3: Matrices and Matrix Algebra
- Lecture 4: Matrices and Matrix Algebra, Cont'd
- Lecture 5: Solving Linear Equations
- Lecture 6: Inverses of Matrices
- Lecture 7: Subspaces of
**R**^{n} - Lecture 8: Sample Exam for Chapter 1
- Lecture 9: Linear Independence and Dimension
- Lecture 10: The Rank of a Matrix
- Lecture 11: Linear Transformations and Matrices
- Lecture 12: Determinants
- Lecture 13: Eigenvalues and Eigenvectors
- Lecture 14: Diagonalization
- Lecture 15: Change of Bases
- Lecture 16: Orthogonality
- Lecture 17: The Gram-Schmidt Algorithm
- Lecture 18: Abstract Vector Spaces and Concrete Examples
- Lecture 19: Coordinatization of Vectors
- Lecture 20: Linear Transformations

- Sample 1st Exam
- Sample 2nd Exam
- Sample Final Exam #1
- Sample Final Exam #2