Linear Algebra is one of the coolest and most useful math courses you can take. Basically , it deals with vectors , matrices all the cool stuff you can do with them. Unfortunately, I did not really have a dedicated course on Linear Algebra in my undergrad. From what I hear , most of the CS people I meet (from India) also don’t have this course in their undergrad. Sure we have had some of the topics (like vectors, basic matrices, determinants, Eigenvalues) split across in multiple courses or in our high school ; but not a single,unified course on it.

Linear algebra is useful on its own but it becomes indispensable when your area of interest is AI , Data Mining or Machine Learning. When I took a machine learning course , I spent most of the time learning things in Linear Algebra, adv Calculus or Linear Optimization. In hindsight , machine learning would have been an easy course if I had previously taken courses on Linear Algebra or Linear Optimization.

As a concrete example, I had a hard time understanding the proof of optimality of PCA or the equivalence of different techniques for calculating PCA (eg Eigen space decomposition or SVD etc) . But once I learnt all about basis, dimension , ,Eigen space and Eigen space decomposition, QR decomposition,SVD etc (which are btw taught in any intro course of Linear Algebra) the whole PCA concept looked really really simple and the proofs looked like straight forward algebraic derivations. Oh well, the benefits of hindsight 🙂

Ok, enough on my rant on lack of Linear Algebra in undergrad. After I struggled mightily in my machine learning course, I decided that I had to master Linear Algebra before taking any more advanced courses. I spent the entire winter holidays learning Linear Algebra as I was taking an advanced data mining course this spring. So this blog post is a discussion of my experience.

### Video Resources

Arguably the best resource to learn Linear Algebra is MIT’s OCW course taught by Professor Gilbert Strang . This course are is one the most popular OCW course and so far had more than 1 Million visits . I also searched for alternate courses, but this course wins hands down both for its excellent teaching style and its depth.

The course website is here. It contains around 35 video lectures on various topics. The lecture are available for download both from ITunes and from Internet Archive. If you prefer YouTube, then the playlist for this course is here.

### Books

The recommended book for this course is Introduction to Linear Algebra. 4th ed. by Gilbert Strang. I found the book to be quite costly , even used books for old versions ! I don’t mind buying expensive books (I shell out a lot of money for data mining books , but a rant on it later ) but since I was interested in Linear Algebra primarily to help me master data mining, I preferred the equivalent book Linear Algebra and Its Applications , also by Gilbert Strang. This book had a very similar content to the recommended book but I felt was more fast paced which suited me fine. Also I was able to get an old copy from Amazon for 10 bucks. Sweet ! My only complaint of the book is that the examples and exercises felt a bit disconnected (or should I say, I wasn’t clear of the motivation ? ) from the topics.

If you don’t want to purchase these expensive books , then there is an EXCELLENT free e-book by Professor Jim Hefferon .The book’s website is here , from where you can download the e-book. I have to say, this book really blew me away. It was really intuitive, has excellent (mostly plausible) examples, was slightly more theoretical than Strang’s book with more proofs. It also had a very helpful solution manual , and a LaTeX version of the book. Too good to be true 🙂 I felt this book had a much limited set of topics than Strang’s course/book, (hence this a truly intro book) , but whatever topic it took, it gave it a thorough treatment. Another thing I liked in the book are the exercises – Most of them were excellent. And having a solution manual helped clarify a lot of things given that I was doing essentially a self-study. Thanks Jim !

### Impressions on the Lectures

I felt, overall, the lectures were excellent. They were short (40-50 minutes). So my usual daily schedule was to listen to a lecture, and read the relevant sections in the book , solve the exercises for which the answers are available at the end of book. All these steps took at most 2-3 hours a day. I was also taking notes in LaTeX using Lyx. I have talked about using Lyx previously in this blog post.

I really liked Strang’s teaching style. He often emphasizes intuition , especially geometric intuition rather than proofs. I felt that is how intro courses must be structured. Proofs are important but not before I have a solid understanding of the topics. But I also have to say that the lectures were varying in quality. Some of the lectures were exceptional while some were not so enlightening. But on the whole, I was really glad that he has made the lectures available online. It has certainly helped me learn Linear Algebra.

### Topics

If possible see all the lectures as almost all of them cover important topics. I did and have to say all of them were excellent and useful. But if you are mostly interested in applied Linear Algebra and planning to use it in Data Mining/ Machine learning, then my suggestion will be Lectures 1-11 , 14-22,25,27-29,33. If you are interested watch lectures 30,31 too. Again a better way to learn is to take notes during lectures and solving at least a few exercises in the book. If you have Matlab or Octave then you can verify answers to some other exercises for which solutions are not given.

### Notes

I have taken LaTeX notes for this course but they are a bit scattered and unorganized. Hopefully, I will organize them together and create a single PDF soon. I kind of put it on a lower priority after I noticed that Peteris Krumins’s blog has a partial set of lecture notes for this course. His lecture notes can accessed here . As of now (Jan 30 , 2010) , he has put notes for first 5 lectures although the frequency seems to be a bit slow.

Have fun with Vectors and Matrices !!

on January 30, 2010 at 6:09 pm |vishithanks for getting me into reading linear algebra

on January 31, 2010 at 6:21 am |LucianHi Saravanan Thirumuruganathan,

Thanks for sharing your experience with us.

Lucian

on February 4, 2010 at 10:59 pm |Introduction to PCA – Part 1 « God, Your Book Is Great !![…] good book on Linear Algebra or some video lectures on it. For more details on learning it see my post on Linear Algebra […]

on February 9, 2010 at 10:19 pm |Big Picture of Calculus « God, Your Book Is Great !![…] have talked about Gilbert Strang and his linear algebra course lectures here . The calculus lectures are also excellent. He focuses on the main topics and gives a geometric […]

on May 1, 2012 at 4:14 pm |AnonymousThnx brotha

on July 4, 2012 at 11:23 am |ChristianHello.

I was wondering how long it took you to complete the courses in Calculus and Linear Algebra? Do you think blitzing through it (in about one month, 4-5 hours per day) would be useful?

Cheers.

on July 12, 2012 at 10:14 pm |Deronfantastic. i have been working through the Strang lectures in preparation for some machine learning and data mining courses coming up. Thanks for pointing me towards the relevant lectures. I did notice that you left off #33 on Singular Value Decomposition. I was wondering if you felt that wasnt important, or perhaps the lecture numbers changed. http://archive.org/details/MIT18.06S05_MP4/

on August 2, 2012 at 12:44 pm |samzayeah man, gilbert’s a cool guy

on September 20, 2012 at 5:47 am |AnonymousExtremely helpful. Thanks a lot

on March 30, 2013 at 6:15 pm |Gurmeet Singh MankuMany thanks for explaining Gilbert Strang’s course and recommending books for linear algebra.