Course in Linear Algebra by Gilbert Strang

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 Rn
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


Posted by Kristian


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.


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!

Ron Modesitt

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

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

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