Within the field of mathematics I handle every day linear algebra plays a vital role. Linear algebra is a field of mathematics that studies vectors and vector spaces. On common use of linear algebra is to solve a set of linear equations. Personally I learned it in university using a book by David C. Lay called Linear Algebra and Its Applications. It is a perfectly good book, and I can recommend it if you want to have a book on the topic.

The reason why I bring up the topic, is that I rediscovered a video version a MIT course in linear algebra taught by Gilbert Strang. I found the videos when I first studied to my exam in linear algebra. I think he teaches it in a very understandable manner. All of the videos can be found at Academic Earth. However, I think that the videos there are poor quality, so I have compiled a list of the videos representing the course in a better quality.

In order to understand Linear algebra you will need a basic understanding of vectors and matrices. Not much, but you need to know what a vector is. After seeing the course titles I can see that I should probably review a few of the topics again.

The course is not that fast paced but he is thorough and a good teacher. Each episode is a little under an hour, so prepare to use a weeks worth of work just watching the lectures.

The last thing I will push to you is the linear algebra book by Gilbert Strang, which is also the course material for the video course. It is called Introduction to Linear Algebra. I have embedded the first video for your pleasure, and all the videos are linked below.

Lecture 1 – The Geometry of Linear Equations

Lecture 2 – Elimination with Matrices

Lecture 3 – Multiplication and Inverse Matrices

Lecture 4 – Factorization into A = LU

Lecture 5 – Transposes, Permutations, Spaces R^{n}

Lecture 6 – Column Space and Nullspace

Lecture 7 – Solving Ax = 0: Pivot Variables, Special Solutions

Lecture 8 – Solving Ax = b: Row Reduced Form R

Lecture 9 – Independence, Basis, and Dimension

Lecture 10 – The Four Fundamental Subspaces

Lecture 11 – Matrix Spaces; Rank 1; Small World Graphs

Lecture 12 – Graphs, Networks, Incidence Matrices

Lecture 13 – Quiz 1 Review

Lecture 14 – Orthogonal Vectors and Subspaces

Lecture 15 – Projections onto Subspaces

Lecture 16 – Projection Matrices and Least Squares

Lecture 17 – Orthogonal Matrices and Gram-Schmidt

Lecture 18 – Properties of Determinants

Lecture 19 – Determinant Formulas and Cofactors

Lecture 20 – Cramer’s Rule, Inverse Matrix, and Volume

Lecture 21 – Eigenvalues and Eigenvectors

Lecture 22 – Diagonalization and Powers of A

Lecture 23 – Differential Equations and exp(At)

Lecture 24 – Markov Matrices; Fourier Series

Lecture 24b – Quiz 2 Review

Lecture 25 – Symmetric Matrices and Positive Definiteness

Lecture 26 – Complex Matrices; Fast Fourier Transform

Lecture 27 – Positive Definite Matrices and Minima

Lecture 28 – Similar Matrices and Jordan Form

Lecture 29 – Singular Value Decomposition

Lecture 30 – Linear Transformations and Their Matrices

Lecture 31 – Change of Basis; Image Compression

Lecture 32 – Quiz 3 Review

Lecture 33 – Left and Right Inverses; Pseudoinverse

Lecture 34 – Final Course Review

Enjoy!

This is awesome.

Thanks for sharing.

I wont start learning Linear Algebra for another one and a half year, in school, so this will give me a good head start.

Hi, Firstly, thanks for sharing the links to the video lectures. Secondly, I would like to know your opinion on which of the two books – David Lay vs Gilbert Strang for linear algebra is better. I come from a CS background and am looking to fill in a few gaps on this topic. Any suggestions and/or recommendations are greatly appreciated.

Thanks!

Hi Prashant.

You are very welcome, all I did was link to them after all. Regarding the books. I don’t think I can recommend one over the other. When I studied linear algebra at university we used Lays book. But I think there has been a few revisions since then. I think it is a pretty good book. However, when studying for finals, several people I know watched Strang’s lectures (probably an earlier version of this course) and some also bought his book and praised it.

If you intend to watch Strang’s lectures here, I think there are pros and cons of using his book. The pro is that it probably follows the course somewhat (and is part of the syllabus). The con is that it explains the things in the same way. So by using Lay’s book you will likely get a second explanation of the same subject, which I personally think is a good thing to get for some topics.

I hope this helps you to decide.

I see. That helps. Thanks again!

Many thanks for digging out the better quality video’s.

One important topic left uncovered in his lectures are inner product spaces