Calendar
Linear Transformations
- Oct 21
- Linear transformations
- Pre-reading
- Worksheet
- Oct 26
- Linear transformations in bases
- Pre-reading
- Worksheet
- HW 9 due
- Oct 28
- Isomorphisms
- Pre-reading
- Worksheet
- Nov 2
- Kernels and ranges for linear transformations
- Pre-reading
- Worksheet
- HW 10 due
- Nov 4
- Eigenvectors and diagonalizability
- Pre-reading
- Worksheet
- Nov 9
- Determinants
- Pre-reading
- Worksheet
- HW 11 due
- Nov 11
- Cofactor expansions
- Pre-reading
- Worksheet
- Nov 16
- Determinants and volumes
- Pre-reading
- Worksheet
- HW 12 due
- Nov 18
- Characteristic polynomials
- Pre-reading
- Worksheet
- Nov 23
- Diagonalization over $\mathbb{C}$
- Pre-reading
- Worksheet
- HW 13 due
- Nov 30
- Cayley-Hamilton
- Pre-reading
- Optional Worksheet
- HW 14 due
- Dec 2
- Jordan Canonical Form
- Pre-reading
- Optional Worksheet
Past topics
Vector Spaces
- Sept 21
- Vector spaces
- Pre-reading: fields, vector spaces
- Worksheet
- Sept 23
- Subspaces and spans
- Pre-reading: subspaces, spans and spanning sets
- Worksheet
- HW 4 due
- Sept 28
- Linear independence
- Pre-reading
- Worksheet
- HW 5 due
- Sept 30
- Bases and dimension
- Pre-reading
- Worksheet
- Oct 5
- Rank
- Pre-reading
- Worksheet
- HW 6 due
- Oct 12
- Inner products
- Pre-reading
- Worksheet
- HW 7 due
- Oct 14
- Gram Schmidt orthogonalization
- Pre-reading
- Worksheet
- Oct 19
- QR decompositions
- Pre-reading
- Worksheet
- HW 8 due
Sage
- Sept 16
- Sage
- Pre-reading
- Class worksheet
Solving Linear Systems
- Aug 24
- Matrices and linear systems
- Pre-readings: introduction, linear equations, systems, vectors, matrices, matrix equations
- Class worksheet
- Aug 26
- Row reduction and reduced row echelon form
- Pre-readings: row echelon form, row operations, row operations and solutions to linear systems
- Class worksheet
- Aug 31
- Gaussian elimination
- Pre-readings: the algorithm, solving systems in row echelon form
- Class worksheet
- HW 1 due
- Sept 2
- Invertibility
- Pre-readings: invertibility
- Class worksheet
- Sept 7
- Equations for solvable systems
- Pre-readings: equations for solvability
- Class worksheet
- HW 2 due
- Sept 9
- LU factorizations
- Pre-readings: LU factorizations
- Class worksheet
- Sept 14
- Geometry of linear systems
- Pre-reading
- Class worksheet
- HW 3 due
Welcome and Orientation
- Aug 19
- Introducing the course and ourselves