Fall 2022
- MATH 323-502: Linear Algebra
Time and venue: TR 12:45–2:00 p.m., BLOC 163
Office hours (BLOC 301b):
- TR 11:00 a.m.–12:00 p.m.
- by appointment
Office hours (ZOOM meeting):
- Wednesday 5:00–6:00 p.m.
- by appointment
Help sessions for MATH 304 (BLOC 133):
- Tuesday 5:00–7:00 p.m.
- Thursday 4:00–7:00 p.m.
Help sessions for MATH 304 (online at MLC):
- Monday 4:00–5:30 p.m.
- Wednesday 4:00–5:00 p.m.
Help sessions for MATH 323 (online at MLC):
- Tuesday 4:00–5:30 p.m.
- Wednesday 4:00–5:30 p.m.
Office hours during the finals (ZOOM meeting):
- Friday, December 9, 5:00–6:00 p.m.
- Monday, December 12, 5:00–6:00 p.m.
- by appointment
Office hours during the finals (BLOC 301b):
- Tuesday, December 13, 11:00 a.m.–1:00 p.m.
Test 2: Thursday, November 17 (Sample problems)
Final exam: Wednesday, December 14, 8:00-10:00 a.m. (Sample problems)
Course outline:
Part I: Elementary linear algebra
- Systems of linear equations
- Gaussian elimination, Gauss-Jordan reduction
- Matrices, matrix algebra
- Determinants
Leon/de Pillis: Chapters 1-2
Lecture 1: Systems of linear equations.
Lecture 2: Gaussian elimination. Gauss-Jordan reduction.
Lecture 3: Gauss-Jordan reduction (continued). Applications of systems of linear equations. Matrix algebra.
Lecture 4: Matrix multiplication. Diagonal matrices. Inverse matrix.
Lecture 5: Inverse matrix (continued).
Lecture 6: Matrix algebra (continued). Determinants.
- Leon/de Pillis 1.4-1.5, 2.1
Lecture 7: Determinants (continued).
Lecture 8a: Determinants (continued).
Part II: Abstract linear algebra
- Vector spaces
- Linear independence
- Basis and dimension
- Coordinates, change of basis
- Linear transformations
Leon/de Pillis: Chapters 3-4
Lecture 8b: Vector spaces.
Lecture 9: Vector spaces (continued). Subspaces of vector spaces.
Lecture 10: Span. Spanning set. Linear independence.
Lecture 11: Linear independence (continued). Basis and dimension.
Lecture 12: Review for Test 1.
- Leon/de Pillis 1.1-1.5, 2.1-2.2, 3.1-3.4
Lecture 13: Basis and dimension (continued). Rank of a matrix.
Lecture 14: Rank of a matrix (continued). Basis and coordinates.
Lecture 15: Change of basis. Linear transformations.
Lecture 16: Linear transformations (continued). General linear equations.
Lecture 17: Matrix of a linear transformation. Similar matrices.
Lecture 18a: Similar matrices (continued).
Part III: Advanced linear algebra
- Eigenvalues and eigenvectors
- Diagonalization
- Orthogonality
- Inner products and norms
- The Gram-Schmidt orthogonalization process
Leon/de Pillis: Sections 5.1-5.6, 6.1, 6.3
Lecture 18b: Eigenvalues and eigenvectors.
Lecture 19: Eigenvalues and eigenvectors (continued). Diagonalization.
Lecture 20: Diagonalization (continued). Euclidean structure in Rn. Orthogonality.
- Leon/de Pillis 5.1-5.2, 6.3
Lecture 21: Orthogonal complement. Orthogonal projection. Least squares problems.
Lecture 22: Review for Test 2.
- Leon/de Pillis 3.4-3.6, 4.1-4.3, 5.1-5.3, 6.1, 6.3
Lecture 23: Norms and inner products.
Lecture 24a: Orthogonality in inner product spaces. The Gram-Schmidt process.
Part IV: Topics in applied linear algebra
- Matrix exponentials
- Rigid motions, rotations in space
- Orthogonal polynomials
Leon/de Pillis: Sections 5.7, 6.2, 6.4
Lecture 24b: Orthogonal polynomials.
Lecture 25: Complexification. Orthogonal matrices. Rigid motions.
Lecture 26: Review for the final exam.
- Leon/de Pillis 1.1-1.5, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.4