Lecture Videos
In Fall 2020, I recorded a series of video lectures on Linear Algebra, to accompany this course 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 Links to an external site., 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.
I have reordered the videos to match the way we currently break the course into weeks, which is somewhat different from the subdivision that we used in 2020. One awkward thing is that what are now weeks two and three were one week back then, and the videos that were recorded for that week can't be split neatly into two portions.
Week 1
- Introduction to linear algebra
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- Putting equations into row reduced echelon form
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- Using row reduced echelon form
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(slides)
Weeks 2 and 3
- Matrix operations
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- Why do we multiply matrices the way we do?
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- Geometry of linear maps
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- Formulas for particular linear maps
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Week 4
- Image and kernel
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- Subspaces
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- Linear dependence and independence
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- Eliminating redundant vectors, and bases
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Week 5
- Bases
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- Dimension
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- Coordinates
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Week 6
Review week, no new videos
Week 7
- Dot products
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- Orthonormal bases
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- Orthogonal projection
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- The Gram-Schmidt algorithm
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(slides)
Week 8
- QR decomposition
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- The method of least squares
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- Least squares and data fitting
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Week 9
- Properties of determinants
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- Geometry of determinants
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- Formulas for determinants
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Week 10
Review week, no new videos
Week 11
- Introduction to eigenvalues and eigenvectors
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- Computing eigenvalues and eigenvectors
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- Formulas for powers of matrices
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- Complex eigenvalues
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Week 12
- Diagonalization
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- Eigenbases
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- Algebraic and geometric multiplicity
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- Algebraic and geometric multiplicity: proofs
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Week 13
- Eigenvectors of symmetric matrices
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- Singular value decomposition
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- How to compute singular value decomposition
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- How to use singular value decomposition
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- Why do matrices have singular value decompositions? Optional, but awesome!
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