Fall 2023

Time and venue:  TR 12:45–2:00 p.m., BLOC 163

First day hand-out

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:
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.

Homework assignment #1 (due Thursday, August 31)

Homework assignment #2 (due Thursday, September 7)

Homework assignment #3 (due Friday, September 15)

Homework assignment #4 (due Friday, September 22)

Homework assignment #5 (due Friday, September 29)

Test 1: Thursday, October 5 (Sample problems)

Homework assignment #6 (due Friday, October 13)

Homework assignment #7 (due Friday, October 20)

Homework assignment #8 (due Friday, October 27)

Homework assignment #9 (due Friday, November 3)

Homework assignment #10 (due Friday, November 10)

Test 2: Thursday, November 16 (Sample problems)

Homework assignment #11 (due Monday, November 27)

Final exam: Tuesday, December 12, 8:00–10:00 a.m. (Sample problems)

Course outline:

Part I: Elementary linear algebra


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.
Lecture 7: Properties of determinants. Evaluation of determinants.
Lecture 8a: Determinants (continued).

Part II: Abstract linear algebra


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.
Lecture 14: Rank of a matrix (continued). Basis and coordinates.
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


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.
Lecture 24: Inner products. Orthogonality in inner product spaces.

Part IV: Topics in applied linear algebra


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.