Lecture Notes
- Below are links to rough lecture notes. They are
meant to be convenient, but not definitive. In particular, there may
be (lots of!) typos. Please inform your instructor of typos and other errors.
Karp Lectures
- Lecture 1: Vectors and the Dot Product
- Lecture 2: Projections and Planes
- Lecture 3: Systems of Linear Equations
- Lecture 4: Gaussian Elimination
- Lecture 5: Linear Independence and Span
- Lecture 6: Linear Independence Continued and Matrix Operations
- Lecture 7: Invertible Matrices
- Lecture 8: Fundamental Theorem of Invertible Matrices
- Lecture 9: Subspaces
- Lecture 10: Bases, Dimension and Rank
- Lecture 11: Linear Transformations
- Lecture 12: Determinants
- Lecture 13: Eigenvalues and Eigenvectors
- Lecture 14: More Eigenvalues and Eigenvectors
- Lecture 15: Diagonalization
Kindred Lectures
- Lecture 1: Big Ideas of Linear Algebra
- Lecture 2: Dot Product
- Lecture 3: Solving Linear Systems
- Lecture 3: Video file for Lecture 3.
- Lecture 4: Solving Linear Systems
- Lecture 5: Homogeneous Systems and Rank
- Lecture 6: Spanning Sets and Linear Independence
- Lecture 7: Matrices, Transposes and Inverses.
- Matrix Multiplication: Video file for Matrix Multiplication
- Lecture 8: Matrix Inverses
- Lecture 9:
- Lecture 10: Subspaces, Bases, Dimension and Rank
- Lecture 11: Rank and Linear Transformations
- Lecture 11: Video File for Lecture 11
- Lecture 12: Video File for Lecture 12
- Lecture 12: Linear Transformations and Determinants
- Lecture 13: Determinants and Eigenvalues
- Lecture 14: Eigenvalues and Eigenvectors
- Lecture 15: Similarity and Diagonalizability
- Lecture 16: More on Diagonalizability; Encodings and Change of Basis