In this course, you will :
- Learn a general algorithm for solving equation systems.
- Learn about the concept of a space within a space.
- Discover how to identify redundant vectors.
- What is the unit of measurement for the size of a vector space?
- Discover how to convert vectors into... other vectors.
- Discover the intricate relationship between linear transformations and matrices.
- Discover a straightforward test for matrix invertibility.
- Investigate some beautiful and useful determinant properties.
- Learn how to work with important special vectors.
- Discover a foolproof method for calculating eigenvalues.
1. Linear Equations
- Two Linear Equations in Two Unknowns
- Three Unknowns
- Gaussian Elimination
- The Full Story of Gaussian Elimination
2. Vector Spaces
- Vector Spaces
- Subspaces and Span
- Linear Independence
- Basis and Dimension
3. Properties of Matrices
- Matrix Algebra
- Inverses and Systems of Equations
- Four Fundamental Subspaces
- Adjacency Matrices
4. Linear Maps and Matrices
- Linear Transformations
- Properties of Linear Transformations
- 2x2 Determinants
- Determinants in Higher Dimensions
5. Eigenvalues and Diagonalizability
- Eigenvalues and Eigenvectors
- Characteristic Polynomial
- PageRank and Exponentiation