Weekly Topics Schedule
Below is a tentative list of topics to be covered each week during the semester. Please note that this schedule serves as a guide and may be revised as the term progresses to better suit the needs of the class or unforeseen circumstances.
- Week 1
- What is linear algebra about?
- Linear equation, Linear system, Three fundamental questions
- Nice and super nice linear systems
- equivalent linear systems, Legitimate operations
- Week 2
- Matrix, Augmented matrix, Coefficient matrix
- Elementary row operations, Row equivalent matrices
- Echelon form, Reduced echelon form, Pivot position, Pivot column
- Row reduction algorithm (RRA)
- Week 3
- Free variables, Basic variables, How to answer the fundamental questions
- Vectors in R^n
- Length of a vector, Addition, Scalar multiplication
- Week 4
- Linear combination
- Span
- How to express a linear system in the language of vectors
- Week 5
- Product of a matrix and a vector
- Matrix equation Ax=b
- More about span and its relation to linear systems
- Week 6
- Homogeneous vs nonhomogeneous systems
- Week 7
- Linearly independent sets
- Vector spaces, subspaces
- Week 8
- Basis for a vector space
- Dimension for a vector space
- Week 9
- Column space, Null space, Row space
- The rank theorem
- Week 10
- Matrix terminology
- Matrix multiplication
- Properties and "nonproperties" of matrix multiplication
- Week 11
- The transpose of a matrix
- Powers of a matrix
- Invertible matrices, inverse of a matrix
- Week 12
- Determinant of a square matrix
- How to compute detA by cofactor expansion
- How to compute detA by row reduction
- Important properties of determinants
- Week 13
- Eigenvalues, Eigenvectors
- Eigenvalue decomposition
- Week 14
- Functions between vector spaces
- Linear transformations, Matrix transformations
- Week 15
- Least-Squares problems