Linear Algebra Lecture Videos
Module Overview
Dear MAT188 students,
I’ve taught MAT188 many times. The EdTech office generously video-captured many of my lectures to be shared with the MAT188 students. Although the course format has changed (from 13 weeks to 12, to a different book, etc.), I’m happy to share lecture videos from 2016 and 2017 with you in case they’re of any use.
We were using a different book in those years and so while I’ve tried to put the videos into a good order for you, some of the videos are Frankenvideos — bits of lectures from different lectures edited together. I’ve also referenced the lectures as closely as I could to the various sections of the textbook “Linear Algebra with Applications” (version 2021, revision A) by W. Keith Nicholson. This book is an open textbook, provided by Lyryx.
The auto-subtitle feature on youtube works surprisingly well, if you need subtitles. It’s not perfect but it’s pretty good if you need a little help parsing what I say in the video. I misspeak on occasion and when this happened in class (and hence in the videos) I tried to point this out using italics in the comments (downloadable as a document file) so that it’s clear that I misspoke. If you find what you believe to be unidentified mistakes, please email me and let me know.
Note: In the YouTube video descriptions, I didn’t have a way of indicating vectors using an arrow over a letter and so vectors are written in italics. Also, I sometimes used MATLAB notation to represent specific vectors and matrices and I used notation like “^2”, “^T”, and “^{-1}” to indicate superscripts. I hope things are relatively clear from context. YouTube’s video description also didn’t allow for links, so please refer to the table below or to the downloadable comments document for links to other resources mentioned.
I love linear algebra and I hope you discover its beauty as well!
Sincerely,
Mary Pugh
mpugh@math.utoronto.ca
Professor, Mathematics
Related Project Resources
| Type | Title | Description |
|---|---|---|
| File | Linear Algebra Lecture Video Descriptions (DOCX, 90KB) | Notes and comments for all of the lecture videos with links to the videos |
| Video | Lecture 1: An Introduction to Linear Systems (Nicholson, Section 1.1) Watch on Youtube or MyMedia | (Duration: 26:50) |
| Video | Lecture 2: Linear Systems: Solutions, Elementary Operations (Nicholson, Section 1.1) Watch on Youtube or MyMedia | (Duration: 42:50) |
| Video | Lecture 3: How to solve a system of linear equations (Nicholson, Section 1.2) Watch on Youtube or MyMedia | (Duration: 50:57) |
| Video | Lecture 4: Reduced Row Echelon, Rank, Solutions (Nicholson, Section 1.2) Watch on Youtube or MyMedia | (Duration: 46:04) |
| Missing lecture: The next thing in Nicholson’s book is Section 1.3 “homogeneous systems of linear equations; trivial and non-trivial solutions; linear combinations of solutions; basic solutions”. In the previous book and in the lectures from Fall 2016 and Fall 2017, these concepts were introduced but were interwoven with other material which you haven’t been introduced to yet. There’s no way to disentangle the material and so I have no lecture videos to offer you on the topic. | ||
| Video | Lecture 5: Vectors, dot products, solutions of Ax=b (Nicholson, Sections 4.1 & 4.2) Watch on Youtube or MyMedia | (Duration: 27:45) |
| Video | Lecture 6: Introduction to Planes (Nicholson, Section 4.2) Watch on Youtube or MyMedia | (Duration: 15:06) |
| Video | Lecture 7: Projection onto a vector, Projection perpendicular to a vector (Nicholson, Section 4.2) Watch on Youtube or MyMedia | (Duration: 47:51) |
| Video | Lecture 8: Review of projections, Introduction to the cross product (Nicholson, Section 4.2) Watch on Youtube or MyMedia | (Duration: 49:52) |
| Video | Lecture 9: Properties and Uses of the Cross Product (Nicholson, Section 4.3) Watch on Youtube or MyMedia | (Duration: 48:23) |
| Video | Lecture 10: Matrix Addition, Scalar Multiplication, Transposition (Nicholson, Section 2.1) Watch on Youtube or MyMedia | (Duration: 21:02) |
| Video | Lecture 11: Matrix Transformations (Nicholson, Section 2.2) Watch on Youtube or MyMedia | (Duration: 28:32) |
| Video | Lecture 12: Introduction to Matrix Multiplication (Nicholson, Section 2.3) Watch on Youtube or MyMedia | (Duration: 13:46) |
| Video | Lecture 13: Introduction to Matrix Inverses (Nicholson, Section 2.4) Watch on Youtube or MyMedia | (Duration: 47:53) |
| Video | Lecture 14: Properties of Inverse Matrices, Invertible Matrix Theorem (Nicholson, Section 2.4) Watch on Youtube or MyMedia | (Duration: 47:08) |
| Here's a nice video on Linear Transformations and how to present linear transformations using matrices (i.e. as a matrix transformation) by 3Blue1Brown. It’s really worth watching even if we can’t present the graphics this way in class, in the book, or on the exams… The previous book focused more on linear transformations than the current book. And so there’re more lectures on the subject than you likely saw. Either the extra lectures below are helpful for you or they’re overkill… | ||
| Video | Lecture 15: Introduction to Linear Transformations (Nicholson, Section 2.6) Watch on Youtube or MyMedia | (Duration: 13:38) |
| Video | Lecture 16: Geometric examples of Linear Transformations (Nicholson, Section 2.6/4.4) Watch on Youtube or MyMedia | (Duration: 48:48) |
| Video | Lecture 17: Representing Linear Transformations as Matrix Transformations (Nicholson, Section 2.6/4.4) Watch on Youtube or MyMedia | (Duration: 50:39) |
| Video | Lecture 18: Composition of Linear Transformations (Nicholson, Section 2.6/4.4) Watch on Youtube or MyMedia | (Duration: 25:01) |
| Video | Lecture 19: Introduction to Determinants (Nicholson, Section 2.6/4.4) Watch on Youtube or MyMedia | (Duration: 40:57) |
| Video | Lecture 20: Elementary row operations and determinants (Nicholson, Section 3.1) Watch on Youtube or MyMedia | (Duration: 50:56) |
| Video | Lecture 21: Usefulness of the determinant: invertibility and geometry (Nicholson Section 3.2/Section 4.4) Watch on Youtube or MyMedia | (Duration: 49:15) "Standard Matrix" |
| Video | Lecture 22: Powers of matrices, introduction to eigenvalues & eigenvectors (Nicholson Section 3.3) Watch on Youtube or MyMedia | (Duration: 47:44) |
| Video | Lecture 23: How to find eigenvalues and eigenvectors (Nicholson Section 3.3) Watch on Youtube or MyMedia | (Duration: 49:24) |
| Video | Lecture 24: Introduction to Diagonalization (Nicholson Section 3.3/Section 5.5) Watch on Youtube or MyMedia | (Duration: 50:11) |
| Video | Lecture 25: Introduction to Systems of Linear ODEs (Nicholson Section 3.5, Optional) Watch on Youtube or MyMedia | (Duration: 49:37) |
| Video | Lecture 26: Systems of Linear ODEs --- where do the solutions come from? (Nicholson Section 3.5) Watch on Youtube or MyMedia | (Duration: 44:11) |
| Video | Lecture 27: Introduction to linear combinations (Nicholson Section 5.1) Watch on Youtube or MyMedia | (Duration: 22:18) |
| Video | Lecture 28: Subsets, Subspaces, Linear Combinations, Span (Nicholson Section 5.1) Watch on Youtube or MyMedia | (Duration: 46:27) |
| Video | Lecture 29: Linear Dependence, Linear Independence (Nicholson Section 5.2) Watch on Youtube or MyMedia | (Duration: 58:21) |
| Video | Lecture 30: More on spanning and linear independence (Nicholson Section 5.2) Watch on Youtube or MyMedia | (Duration: 50:02) |
| Video | Lecture 31: Bases, finding bases for R^n (Nicholson Section 5.2) Watch on Youtube or MyMedia | (Duration: 1:01:52) |
| Video | Lecture 32: Subspaces Related to Linear Transformations (Nicholson Section 5.4) Watch on Youtube or MyMedia | (Duration: 23:20) |
| Video | Lecture 33: Introduction to Solution space, Null space, Solution set (Nicholson Section 5.4) Watch on Youtube or MyMedia | (Duration: 48:37) |
| Video | Lecture 34: Introduction to range of a linear transformation, column space of a matrix (Nicholson Section 5.4) Watch on Youtube or MyMedia | (Duration: 50:55) |
| Video | Lecture 35: Null(L), Range(L), the rank theorem, Row(A) (Nicholson Section 5.4) Watch on Youtube or MyMedia | (Duration: 50:55) |
| Video | Lecture 36: Introduction to Sets of Orthogonal Vectors (Nicholson Section 5.3/Section 8.1) Watch on Youtube or MyMedia | (Duration: 53:20) |
| Video | Lecture 37: More on diagonalization (Nicholson Section 5.5) Watch on Youtube or MyMedia | (Duration: 48:40) |
| Video | Lecture 38: Best Approximate Solution of a Linear System (Nicholson Section 5.6) Watch on Youtube or MyMedia | (Duration: 47:49) Spurious Correlations webpage |
| Video | Lecture 39: Introduction to Orthogonal Subspaces (Nicholson Section 8.1) Watch on Youtube or MyMedia | (Duration: 50:36) |
| Video | Lecture 40: How to project onto a subspace (Nicholson Section 8.1) Watch on Youtube or MyMedia | (Duration: 48:50) |
| Video | Lecture 41: Introduction to the Gram-Schmidt process (Nicholson Section 8.1) Watch on Youtube or MyMedia | (Duration: 47:53) |
| Video | Lecture 42: Finishing up the Gram-Schmidt process (Nicholson Section 8.1) Watch on Youtube or MyMedia | (Duration: 35:56) Solving the Normal Equations by QR and Gram-Schmitd The modified Gram-Schmidt procedure Gram-Schmidt Orthogonalization: 100 Years and More |
| Video | Lecture 43: Non-diagonalizable matrices examples; all symmetric matrices are diagonalizable (set-up for Nicholson Section 8.2) Watch on Youtube or MyMedia | (Duration: 37:20) |
| Video | Lecture 44: How to orthogonally diagonalize a symmetric matrix (Nicholson Section 8.2, optional) Watch on Youtube or MyMedia | (Duration: 51:37) |
