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MIT 18.06 Linear Algebra - Spring 2005   

MIT 18.06 Linear Algebra Spring 2005

Course Highlights

This course features a complete set of video lectures by Professor Gilbert Strang. There are also Java applets with sound as well as interactive Java applets. The text for this class is Introduction to Linear Algebra by Gilbert Strang.

Course Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Course Homepage 18.06 Linear Algebra Spring 2005

Course features at MIT OpenCourseWare page:

Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET


Unit I: Ax = b and the Four Subspaces

Unit II: Least Squares, Determinants and Eigenvalues

Unit III: Positive Definite Matrices and Applications

Final Course Review

Reviews and comments:

Comment1 Alessandro Biancardi, March 7, 2009 at 5:23 p.m.:

I'm italian quantum chemist and I'm very happy, because with this lecture I can recross a lot of things. Thanks.

Comment2 sherwin tumaliuan, March 17, 2009 at 3:50 a.m.:

i'm a filipino and i'm planning to go back to college this semester so i can finish my elctronics and communications engineering . i was hoping that thru this open courseware i'l be able to review an almost a decade backlog of study. is there a way to download a single file compilation of these lectures? thanks

Comment3 William, March 27, 2009 at 2:17 a.m.:

yes, go to, this site offers download for each video

Comment4 S Shnyder, May 6, 2009 at 1:01 a.m.:

I can watch this just to recall learnings from college (one of my math professors was from MIT). Its just like having a math professor at home, anytime I want. Thanks

Comment5 ernesto, May 13, 2009 at 3:26 a.m.:

please to inform with respect to video readings to me into english to grammar Gracias.

Comment6 Andrew Cho, June 4, 2009 at 8:01 a.m.:

Wow. I am so impressed. The undergraduate education at MIT is is incredible. I am determined to apply to MIT for my grad school. This professor is the real deal- I see so much passion in Prof. Strang.

Comment7 Dawn King, July 20, 2009 at 2:07 p.m.:

just perfect~~MIT is a heaven for scientific and mathematical study. i will try to go through all the video courses on this website.

Comment8 Oliver Qi, July 25, 2009 at 8:02 a.m.:


Comment9 Melvyn Massoumi G., August 31, 2009 at 10 a.m.:

It is adorable to see MIT opening the courses to the public. I am a 21 year old Iranian student and I find everything here in great explanations and by following my own syllabuses I get to learn the most I can. Thanks to MIT and All the lecturers. God Bless You

Comment10 Daniel, September 1, 2009 at 10:54 a.m.:

Dear Professor Strang,
thank you for those great lectures! your lecture helped me to get a better understanding of the svd.
best regards

Comment11 Dattatreya, September 28, 2009 at 9:53 a.m.:

This guy is awesome, i have seen all the videos ....looks like 10 years down the line people will not sign up for full time courses ...thanks MIT

Comment12 Manesh, September 29, 2009 at 1:22 p.m.:

Thanks to MIT. This is just what I wanted. I wish I had a professor like Prof Strang

Comment13 Hassan, December 24, 2009 at 12:27 a.m.:

Thanks to MIT. Really It is wonderful lectures and wonderful lecturers.
HAPPY NEW YEAR everybody!

Comment14 bmt, January 7, 2010 at 12:03 a.m.:

It is really very good to have such open lectures, from best
professors for the better america and as well for the better world.
I had took this course before, but you give it a life to it.

thank you.

Comment15 jaysan h shukla, January 13, 2010 at 2:30 p.m.:


Comment16 Hongmei Yao, January 15, 2010 at 4:24 a.m.:

Very good, it is so important for me to teach and learning, Thank you very much. When i find these materials, i feel very very happy. Thanks again, it is really helpful for me.

Comment17 Sheece Gardezi, January 20, 2010 at 9:33 p.m.:

Thanks a million MIT is the best!

Comment18 Ou Zhang, January 23, 2010 at 2:53 a.m.:

This is amazing! MIT rocks!

Comment19 pablo monat, April 9, 2010 at 4:43 a.m.:

Dear Professor Strang,
thank you very much for those lectures! I have enjoyed them greatly. And you made me fan of Liner Algebra instead of Calculus...
best regards

Comment20 sara, April 25, 2010 at 6:34 a.m.:

I'm Chinese-American Computer Scientist. In fact, I started out as an Mathematics major and then switched to Computational mathematics. I love math.

I'm extremely exciting about finding this material, because it is the best Liner Algebra course I ever take. I appreciate its beauty. Sometimes I got so exciting that I explained it to my mother on Labor day.

Thanks Gilbert, Live Long and Healthy.

Comment21 Gianfranco Oldani, May 22, 2010 at 9:28 p.m.:

Thanks a LOT Gilbert for this material. For me also it's probably the most interesting, the most exiting, the most pedagogical and full of conceptual ideas course in linear algebra I've ever listen. Every professor should listen what teaching mean by looking at your lessons.

Thanks again a lot

Warm Regards

PS: why so few courses like this online...

Comment22 Shan, June 9, 2010 at 12:32 p.m.:

Thank Professor Strang...You r really doing a gr8 job. Thank you .

Comment23 André Martins Vaz, August 20, 2010 at 4:58 a.m.:

I'm a brazilian student of engineering from UFMG. I'm very glad and thankfull for the OCW. This way, I can learning things related to my course and improoving my english at the same time. Sorry if I commited any mistake. Thanks Mr Strang.

Comment24 emily, September 27, 2010 at 5:53 a.m.:

As a foreign student graduated years ago and wants to go back to school, the OCW is a wonderful site for me. I could learn freely after work, download to my computer, do the reading at the same time watching the video and improve English as well! Thanks Dr. Strang! Your class is gorgeous and it's easy to understand the complex conceptions!

Comment25 A. Joseph Antony, November 29, 2010 at 8:44 a.m.:

I am planning to pursue my research in image processing, when I was looking for some materials to refresh the basic concepts of linear algebra, I came across this lecture series.... wow, excellent. Prof. Strang is great, the way he simplifies the complex concepts... Hats off to him...

Comment26 mohammad, December 8, 2010 at 8:46 p.m.:

I'm an Iranian civil engineer and I love math.In fact, I started out as desighner but now I'm very interested in math that I am going to study math. it is the best course I ever seen. I appreciate its beauty. Sometimes I got so exciting that I explained it to my son.
Thanks prof. Gilbert, Live Long and Healthy.

Comment27 Nanda Kumar, January 25, 2011 at 9:32 a.m.:

Oh.......! Mr. Strang your lectures are really great.......!!!!!

Comment28 Inthakesone, March 8, 2011 at 5:20 a.m.:

I spent a lot of time to finish this lectures. It is really great to burn my time by looking his lectures.

Comment29 David, April 9, 2011 at 11:15 a.m.:

It is so great that it helps me better understand linear algebra, and even mathematics. Thanks, Prof. Strang.

Comment30 huqunwei, September 2, 2011 at 12:17 p.m.:

I am very happy.this teacher is very good.since I lisen to his courses ,I gain more form liner Algebra.Thankes for MIT,thankes for Professor Strang.

Comment31 Safwan, October 11, 2011 at 10:11 a.m.:

Prof.Strang & MIT the world is in-debt to you & America.
Masha Allah :-)

Comment32 Jorge Gaona, November 21, 2011 at 4:44 a.m.:


Comment33 Samat, December 1, 2011 at 12:21 a.m.:

I am from Kazakhstan and i very happy that i can meet MIT lecture, thank you very much!!!

Comment34 John Kamanja, December 19, 2011 at 10:31 a.m.:

I am Kenyan living in South Africa and studying at UNISA BSC Computer Science (long distance). These videos are God-Sent! They fill in gaps in my self study and more importantly I can have my 'class' on the train on my way to work! MiT ROCKS!

Comment35 Anshul Garg, December 22, 2011 at 12:25 p.m.:

I saw this and it made me fall in love with maths all over again. He is simply amazing. Got the textbook. So amazing and lucid. It makes me feel its not these people (MIT scholars) are very different, its just that they view things in such clear uncomplicated way. Thank you very much. Please have more such video lectures for other courses too. Its for the greater good and enhancement of knowledge and ultimately mankind.....

Comment36 Ahtisham Ahmad, May 2, 2012 at 12:04 p.m.:

I am from Pakistan and these lectures have flawed my previous understandings about linear algebra. Being a good mathematician hated LA due to absurd concepts from alot of absurd sources...but an interesting person makes everything interesting.....and today i feel like a expert in LA..

Thanks to Prof.Gilbert...You have made all my complications go away.

Comment37 Garry P. Setiawan, May 27, 2012 at 2:51 p.m.:

I am from Indonesia, and still an undergrad student.
All i want to say is a gratitude.
Thanks God I found your lecture, it helps me a lot understanding the beauty of linear algebra.
Every lecturer of math should sees your way of teaching!

Comment38 Juan C, June 15, 2012 at 4:07 p.m.:

thanks a lot to MIT for letting the whole world to see this magnificent lectures, grettings from Argentina

Comment39 Srinath, July 4, 2012 at 7:05 a.m.:

I am very impressed with his teaching basically i am a game programmer and i am weak in linear algebra and game developement involves equations by seeing this video tutorial i learned many things.The good thing about strang is the way he teaches he goes in depth of each concept and when he teaches he puts a question and tells practical example that makes me understand solution better.strang you r awesome every professor cant teach like this.Many professor till now i had seen they just tell how to use the formulae but no one tells how it comes thats where you stand and thats the reason i like your teaching.

Comment40 Khaing Thandar Hnin, July 10, 2012 at 12:46 p.m.:

I'm from Myanmar, second year (mechatronics,AIT). Thanks a lot Professor Strang.

Comment41 Temo Sabbather, July 18, 2012 at 8:19 a.m.:

Thanks a lot. good work :)

Comment42 monal shrivastava, October 27, 2012 at 1:58 p.m.:

a very conceptual ideas are given by prof. gilbert. The best thing is that,pronounciation is very good. Even indians can also grasp his english very easily. Its like a interesting movie.

Comment43 Larsen, January 4, 2013 at 5:58 a.m.:

this is a great oppurtunity to recross a lot of things learnt and many things that are missed. The style of lecture is great that am never lost in the mid.

Comment44 Thierry, June 24, 2013 at 11:30 p.m.:

We do not have in France professors like that unfortunately !!!
Those are the best online lectures in maths I have ever seen !

Comment45 Shirley, August 16, 2013 at 8:50 a.m.:

Thank you, Prof. Strang. I'm a Chinese, my English name is Shirley. Your lecture is conscise and beautiful. I watch it just as watching an attractive movie. I think I already become your fan now.
Wish you be healthy and happy everyday.

Comment46 yogesh, September 18, 2013 at 4:39 p.m.:


Comment47 rahul gaikar, May 16, 2014 at 6:22 p.m.:

I am rahul gaikar, i just complited my degree in mathematics from modern college pune and trying for entrance of msc in university of pune, these videos of linear algebra are really helpful to me
Thanks, u r exellent sir.

Comment48 Tariq Rasheed, August 5, 2014 at 11:17 a.m.:

I am Tariq, student of Computer Science from Pakistan. I am a big fan of Prof. Strang. This course was really helpful fom me. I got 4 GPA in LA just because of it. I have no words to praise Prof. Strang. I wanna say I love you Sir.

Comment49 Raj, August 18, 2014 at 1:32 p.m.:

The best lectures in the Online World for learning Eigen Values and Vectors.

Comment50 R.Rajaganapathi, June 3, 2015 at 11:47 a.m.:

I am indian , this lecture is very much use full. Thaks to MIT for providing this great professor lecture. MIT is doing very great jog for education thank a lot.

Comment51 ATIKUR RAHMAN, November 9, 2015 at 7:52 p.m.:

I'm Atikur Rahman From Bangladesh. This course is very helpful for me. Thanks a lot.

Comment52 José M. Vera Valerio, December 23, 2015 at 7:18 p.m.:

Iam José, friend of Miguel that last year was knowing you at MIT. I am from Veracruz, Mexico and a professor of Linear Algebra in the Universidad Veracruzana and i use your text book. I want to say thanks a lot for your lectures.

Comment53 Afshin, January 7, 2016 at 2:38 p.m.:

I cant help myself to see this course as a movie series, I am seeing 7 sessions a day. I am not just learning Linear Algebra but also I am learning how to learn and how to teach.
I wish someday I can teach quantum mechanics like you teach linear algebra
Most Sincerely

Comment54 Afshin, January 7, 2016 at 2:39 p.m.:

I cant help myself to not see this course as a movie series, I am seeing 7 sessions a day. I am not just learning Linear Algebra but also I am learning how to learn and how to teach.
I wish someday I can teach quantum mechanics like you teach linear algebra
Most Sincerely

Comment55 hala mostafa, May 6, 2017 at 7:08 p.m.:

thanks a lot prof. strang , your lectures helped me to best understanding of linear algebra.

Comment56 Bruna Megumi, June 16, 2018 at 10:01 p.m.:

I'm from Brazil and I can't watch any videos from mit anymore. I want to know why. I used to watch many videos before, now I can't. Please, if someone can help ...

Comment57 Jen, December 11, 2018 at 9:15 a.m.:

This lecture is very helpful! Now I love math! :) Thank you prof. Strang. That was awesome!

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