- Lecture 1: (The language of sets)
- Lecture 2: (Maps between sets)
- Lecture 3: (Systems of linear equations)
- Lecture 4: (Vector spaces)
- Lecture 5: (Example of vector spaces)
- Lecture 6: ("Proofs" using axioms: properties of vector spaces)
- Lecture 7: (Vector subspaces I)
- Lecture 8: (Vector subspaces II)
- Lecture 9: (Linear combinations)
- Lecture 10: (From linear combinations to linear equations)
- Lecture 11: (Linear independence and dependence I)
- Lecture 12: (Linear independence and dependence II)
- Lecture 13: (From belonging to a span to existence of solutions to linear equations I)
- Lecture 14: (From belonging to a span to existence of solutions to linear equations II)
- Lecture 15: (From belonging to a span to existence of solutions to linear equations III)
- Lecture 16: (Matrices and row operations I)
- Lecture 17: (Matrices and row operations II)
- Lecture 18: (Solving systems of linear equations)
- Lecture 19: (Generating sets)
- Lecture 20: (Bases and coordinates)
- Lecture 21: (Dimension of a vector space)
- Lecture 22: (Linear transformations)
- Lecture 23: (Image of a linear transformation)
- Lecture 24: (Kernel of linear transformation)
- Lecture 25: (From linear transformations to matrices, and back)
- Lecture 26: (Image and kernel of matrices)
- Lecture 27: (The rank-nullity theorem)
- Lecture 28: (From linear transformations to linear equations, and back)
- Lecture 29: (Operations on matrices I)
- Lecture 30: (Operations on matrices II)
- Lecture 31: (Invertible linear transformations)
- Lecture 32: (Determinants)
- Lecture 33: (Eigenvalues and Eigenvectors I)
- Lecture 34: (Eigenvalues and Eigenvectors II)
- Lecture 35: (Eigenvalues and Eigenvectors III)
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