The Big Picture of Linear Algebra

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

A matrix produces four subspaces: column space, row space (same dimension), the space of vectors perpendicular to all rows (the nullspace), and the space of vectors perpendicular to all columns.

License: Creative Commons BY-NC-SA

[ksbalaji]

Prof. Strang gave his final lecture before retirement yesterday. He has touched the lives of millions of students. Please watch his final lecture just to see the emotion filled comments of his students from countries across the world. Thank you, professor!

[yael]

when he emphasized "M-I-T blackboard" i felt that flex.
my professors only use regular blackboards.

[noonansean]

Wish I had seen this when I was taking Linear Algebra. Wonderful short lecture.

[JustinGarfield]

I don't have any degree in math but I have been studying it for 2 years. I just bought a linear algebra book and I find this stuff so fun to do.

[zacharyadler]

The reason it is called the left null space is because it is typically obtained by analyzing vA = 0 which is essentially the same thing he did to calculate the left null space but he presented it differently with transpose of A

[MrSimmies]

Phenomenal lecture as usual from Professor Strang. Thank you sir for your contributions and enjoy your retirement!

[yinghaohu]

Nice Tutorial. I read this in a Linear Algebra book, about 3 years ago. Fortunately I didnt forget them. Until I watch this Video, I understand the concepts and relationships between these spaces.

[clapdrix]

"Only has 1 puny vector..."
Love it

[Jab_hutt]

Just watched it, mind wondered off at the end, but was just pleasant to look and hear. Thanks!:) Legend.

[BGasperov]

what a beautiful metasummary of linear algebra, kudos to prof. Gilbert for the amazing mini lecture.

[apdj]

You can tell how smart he is from the size of his chalk

[Querulus]

I'm here for the actual full picture; a chalkboard wall filled with 'Fermat's Last Theorem' and towards the end of it, a bunch of angry nicks ingrained into the slate.

[JulieIsMe]

Great and amazing prof. Thanks! so rewarding!

[rpitay]

really good teacher but what about linear transportation, determinant etc

[ako]

In our class, we call the left-null space just 'null space'. I don't think I have seen left null space

[tspoon]

Blink with your left eye every time he says something interesting

[kutilkol]

really great! but go with speed 1.25

[johnbigger]

Smh, I see the left nullspace gets treated like a second class citizen again at 10:00

[nicbouchard]

When you didn't study for your final exam and you have 16 minutes left

[IanRichardArko]

Maybe the people at MIT should invent a blackboard that can fit an infinite plane?