Fall 2023
- MATH 323-501: 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:
- Monday 10:00 a.m.–12:00 p.m. (BLOC 357)
- Tuesday 2:00–5:00 p.m. (BLOC 628)
- Wednesday 10:00 a.m.–12:00 p.m. (BLOC 303, BLOC 360)
- Thursday 2:30–5:00 p.m. (BLOC 624)
Office hours during the finals (ZOOM meeting):
- Wednesday, December 6, 5:00–6:00 p.m.
- Friday, December 8, 5:00–6:00 p.m.
- or by appointment
Office hours during the finals (BLOC 301b):
- Monday, December 11, 11:00 a.m.–1:00 p.m.
Test 2: Thursday, November 16 (Sample problems)
Final exam: Tuesday, December 12, 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.
Lecture 4: Matrix algebra. Diagonal matrices.
Lecture 5: Inverse matrix.
Lecture 6: Matrix algebra (continued). Determinants.
- Leon/de Pillis 1.3-1.5, 2.1
Lecture 7: Properties of determinants. Evaluation of determinants.
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: Basis and dimension (continued). Rank of a matrix.
Lecture 13: Review for Test 1.
- Leon/de Pillis 1.1-1.5, 2.1-2.2, 3.1-3.4
Lecture 14: Rank of a matrix (continued). Basis and coordinates.
- Leon/de Pillis 3.2, 3.5-3.6
Lecture 15: Change of basis. Linear transformations.
Lecture 16: Range and kernel. General linear equations. Multiplication by a matrix as a linear map.
Lecture 17: Matrix representation of linear maps. Change of basis for a linear operator. Similar matrices.
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 18: Eigenvalues and eigenvectors.
Lecture 19: Eigenvalues and eigenvectors (continued). Diagonalization.
Lecture 20: Euclidean structure in Rn. Orthogonal complement.
Lecture 21: Orthogonal projection. Least squares problems.
Lecture 22: Orthogonal sets. The Gram-Schmidt orthogonalization process. Norm on a vector space.
Lecture 23: Review for Test 2.
- Leon/de Pillis 3.4-3.6, 4.1-4.3, 5.1-5.3, 5.5-5.6, 6.1, 6.3
Lecture 24: Inner products. Orthogonality in inner product spaces.
Part IV: Topics in applied linear algebra
- Matrix exponentials
- Rigid motions, rotations in space
- Orthogonal polynomials
Leon/de Pillis: Sections 5.5, 5.7, 6.3, 6.4
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, 5.1-5.6, 6.1, 6.3-6.4