See the course calendar for details concerning exams and problem sets.
- Vector Spaces
- Definitions and Examples
- Subspaces
- Linear Independence
- Bases and Finite-Dimensional Vector Spaces
- Important Theorems
- Linear Transformations
- Definitions and Examples
- Kernal and Image
- Useful Theorems
- Isomorphism
- Matrix Representation
- Systems of Linear Equations
- Definition and Basics
- Gauss-Jordan Elimination
- Applications
- Matrix Representations
- Determinants
- Calculation
- Properties
- Relation to Invertibility
- Theorems
- Eigenvalues and Eigenvectors
- Definitions and Examples
- Characteristic Polynomial
- Connections to Differential Equations
- Diagonalization
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