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- Lecture 1: Introduction: Fields and Vector Spaces
- Lecture 2: Subspaces, Linear Dependence and Linear Independence
- Lecture 3: Dimension and Bases
- Lecture 4: Elementary Operations and Matrices
- Lecture 5: Finitely Generated Vector Spaces
- Lecture 6: Systems of Linear Equations
- Lecture 7; Solving Linear Systems
- Lecture 8: Homogeneous Linear Systems
- Lecture 9: Hyperplanes
- Summary of the Basic Definitions and Theorems for Exam 1
- Lecture 10: Linear Transformations
- Lecture 11: Linear Transformations and Matrices
- Lecture 12: Homomorphisms and Isomorphisms
- Lecture 13: Quotient Spaces
- Lecture 14: The Isomorphism Theorems
- Lecture 15: Endomorphisms and Automorphisms
- Lecture 16: Determinants
- Lecture 17: The Theory of A Single Endomorphism (Introduction)
- Lecture 18: Invariant Subspaces
- Lecture 19: The Triangular Form and Cayley-Hamilton Theorems
- Lecture 20:
- Lecture 21: