This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.
- Primary text: "Linear Algebra Done Right", 3rd edition, by Sheldon Axler
- Supplemental text: "Introduction to Linear Algebra", 4th edition, by Gilbert Strang (a course packet option will be available for students who do not wish to buy the entire textbook)
This advanced undergraduate course in linear algebra will be of interest to Math, Computer Science, and Physics majors. It may also be of interest to undergraduates in Engineering and other units.
Review of basic linear algebra [Axler Ch. 1-3] (7 lectures)
New vector spaces from old ones [Axler Ch. 3] (2 lectures)
Eigenvalues and eigenvectors [Axler Ch. 5] (4 lectures)
Inner product spaces and orthogonality [Axler Ch. 6] (3 lectures)
Applications of orthogonality [Strang] (5 lectures)
Operators on inner product spaces [Axler Ch. 7] (6 lectures)
Applications of eigenvalues and eigenvectors [Strang] (6 lectures)
Complex vector spaces and canonical forms [Axler Ch. 8] (5 lectures)
Applications of the Jordan Canonical Form (2 lectures)
Trace and determinant [Axler Ch. 10] (3 lectures)