In Fall 2020, I recorded a series of video lectures on Linear Algebra, to accompany the course Math 214 (Applied Linear Algebra) at the University of Michigan as it went online thanks to COVID-19. I revised the lectures during 2021, with a great deal of help from Michigan student Zhixin Mo, and am now releasing them onto the open internet. I hope these videos will be of use to people studying Linear Algebra, at Michigan and elsewhere.

As a note: This was a 13 week course: The weeks between Week 4 and 5, between Weeks 7 and 8, and after Week 10, were used for review and discussion and had no videos associated to them. Doing it in 10 weeks with no breaks would probably be a bad idea.

Note: This webpage has a second home now on the Canvas page for Math 214. This is in response to UMich requirements that course materials be hosted within Canvas. That page also reorders the videos slightly, to more closely match how they are used in current teaching. I'll try to maintain both pages, but it is possible that they will get further out of sync in time. I plan to keep the videos and slides available to the public indefinitely.

- 1a: Introduction to linear algebra (video) (slides)
- 1b: Putting equations into row reduced echelon form (video) (slides)
- 1c: Using row reduced echelon form (video) (slides)

- 2a: Matrix operations (video) (slides)
- 2b: Why do we multiply matrices the way we do? (video) (slides)
- 2c: Geometry of linear maps (video) (slides)
- 2d: Formulas for particular linear maps (video) (slides)

- 3a: Image and kernel (video) (slides)
- 3b: Subspaces (video) (slides)
- 3c: Linear dependence and independence (video) (slides)
- 3d: Eliminating redundant vectors, and bases (video) (slides)

- 5a: Dot products (video) (slides)
- 5b: Orthonormal bases (video) (slides)
- 5c: Orthogonal projection (video) (slides)
- 5d: The Gram-Schmidt algorithm (video) (slides)

- 6a: QR decomposition (video) (slides)
- 6b: The method of least squares (video) (slides)
- 6c: Least squares and data fitting (video) (slides)

- 7a: Properties of determinants (video) (slides)
- 7b: Geometry of determinants (video) (slides)
- 7c: Formulas for determinants (video) (slides)

- 8a: Introduction to eigenvalues and eigenvectors (video) (slides)
- 8b: Computing eigenvalues and eigenvectors (video) (slides)
- 8c: Formulas for powers of matrices (video) (slides)

- 9a: Diagonalization (video) (slides)
- 9b: Eigenbases (video) (slides)
- 9c: Algebraic and geometric multiplicity (video) (slides)
- 9d: Algebraic and geometric multiplicity: proofs (video) (slides)

- 10a: Eigenvectors of symmetric matrices (video) (slides)
- 10b: Singular value decomposition (video) (slides)
- 10c: How to compute singular value decomposition (video) (slides)
- 10d: How to use singular value decomposition (video) (slides)
- 10e: Why do matrices have singular value decompositions? (video) (slides)