1. The Geometry of Linear Equations

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Published 2019-09-24

MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: ocw.mit.edu/18-06S05
YouTube Playlist: • MIT 18.06 Linear Algebra, Spring 2005

1. The Geometry of Linear Equations

License: Creative Commons BY-NC-SA
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All Comments (21)

@mitocw 4 years ago

Audio channels fixed!
@scottbrandon6244 11 months ago

This was filmed in 2005 when Gil was 70. He just retired from MIT this month (May 2023) at age 88 after a 62 year career as a professor. What a great career.
@sanchayanmaity5731 1 year ago

In two years of junior college and 4 years of engineering, not once did anyone gave the column picture explanation. Mind blown. Thank you, Dr. Strang.
@gerardomoscatelli9035 3 years ago

I wish I had teachers like Prof Gilbert Strang when I studied linear algebra. What a difference makes to have someone dedicated to explaining the geometry of what is going on.
@BC-hg6dz 4 years ago

Thank you Dr. Strang. I graduated from high school functionally illiterate in math. In my journey to teach myself math you have become a great mentor.
@aadarshmishra2504 3 years ago

The cameraman here is now a Senior ML Engineer at Google, California.
@shutupimlearning 1 year ago

its insane that this video is 15+ years old and still so valuable to someone beginning to learn linear algebra like myself
@PhucLe-qs7nx 2 years ago

00:00 Course overview 01:00 Lecture overview 04:25 Row picture 2D 08:35 Column picture 2D 15:38 Row Picture 3D 22:00 Column Picture 3D 27:55 Can I solve Ax=b for all b? 32:25 "Visualise" 9-dimension 35:33 How to multiply a matrix and a vector?
@SatireDaily 4 years ago

humans will start learning machine learning here.
@Christopher-mi6qe 3 years ago

Took 18.06 in 1992 and he taught it. Great stuff, and an awesome professor.
@FHB71 3 years ago

That makes me remember the first semester linear algebra lecture. He certainly takes his time to explain, what the interpretation is and that is wonderful. We were not so lucky unfortunately.
@wlycdgrTheEverydayWorld 4 years ago

Kept 1st lecture intro to one minute. Bless this man.
@omeryacine8281 4 years ago

about to cry of how beautiful this is
@marco.nascimento 3 years ago

An amazing first lecture, glad to see the audio is fixed, thanks for taking care of this course. It's beautiful to perceive people from all over the world gathering here to gain knowledge, Professor Strang is a great teacher <3
@douglasstrother6584 4 years ago

It's so important to develop a geometric view of linear algebra.
@mathyscrete9469 4 years ago

For everyone begining this lectures that have no notions of linear algebra, I reccomend you to watch 3Blue1Brown series before because he put a lot of image on the word. Sorry for the mistakes, I am not an english speaker.
@randomdude354 3 years ago

There are so many moments when I wanted to give this video an extra LIKE! He's such a good teacher!
@graphchick 11 months ago

as a 1st year grad student a very long time ago, i took a course in linear algebra using Gil Strang's book. learning about the relationship between the four fundamental spaces of a matrix felt revelatory at the time, and i still have that book. he's such a wonderful expositor.
@douzijin6541 4 years ago

For a person who is not really good at math, I hope this will really help me to develop a big picture of what linear algebra is. Thanks Prof. Strang.
@MelodyMcQwerty 2 years ago

We're using Professor Strang's book in my linear algebra class and I really cannot understand my professor's teaching style. My friend pointed me to these lectures instead and I already feel like I actually understand a lot more from this one lecture than I have the past two weeks in my class. Thanks Professor Strang!