Part 2: The Big Picture of Linear Algebra

A Vision of Linear Algebra
Instructor: Gilbert Strang

Multiplication by A transforms the row space to the column space. Professor Strang then reveals the Big Picture of Linear Algebra where all four fundamental subspaces interact.

License: Creative Commons BY-NC-SA

[MrFurano]

4:47 "There you go. You can die happy now".

[xahiru]

Orthogonal sounds cooler :-), I love him

[ekarpekin]

In university i had an impression that linear algebra is sort of least interesting subject of maths, maybe not too complicated in general but certainly not cool. When MIT started OCW, ive overlooked LA videos for a long time. Eventually and by an accident i looked into a couple of those from first banch. What a surprise! My biggest respect to Gilbert. Back in 2014 i was in Boston for few days and three times was walking into MIT into his office to thank him in persons, yet alas, he was out of office. Thank you anyway for these great lessons. If someone from MIT reads this, please pass my thanks to Mr Strang (Russia)

[SoumilSahu]

Somehow it doesn't seem right to see him without a chalk in his hand

[jeffery]

4:48 "You can die happy now." -- Prof.Strang, Spring 2020

[alileo]

08:53 I see what you did there, Professor :)

[DistortedV]

Thank you MIT OCW and Gilbert Strang for this series. I have already taken a linear algebra class, but this introductory summary is a great refresher and more detailed/concise than any others on youtube at the moment.

[jonathansum]

Upvote me if you still think writing on the board is better than this.
I used to watch Linear algebra and Diff Eq from Strang to pass the class.

[brandomiranda]

Sorr for being pedantic, but I am not sure I appreciate why A = CR is nicer...Is it mainly because it contains some basis for the column space in C and some basis for the row space in R? I failed to appreciate this new start! haha :(

[johnlocke]

Wait I’m lost now. It’s been years for me. What’s the null space again?

[johnniefujita]

A great thanks to professor strang! Amazing Guy!

[physicsgobrr]

I would say the permutation part needs a little more explanation. But still, what a great lecture!

[에헤헿-lv]

I dont think this lecture was good, if you have a hard time understanding check the lecture with the same title he did six years ago it's much better

[BorisTreukhov]

Can someone explain what is the meaning of the arrows? What do they signify?

[paperhats]

The grand sequel that we didn't deserve yet didn't know how much we needed it

[BleachWizz]

Lol this is so much more intuitive and easy to remember what you want to do than those rules they teach you in school so you can compute stuff and they tell you've learned it

[王甯-hx]

This is just brilliant. So much knowledge is condensed into this 11mins video. Respect!

[wasnloshier]

Is the correctnes of A=LU proved by induction?

[aikenji]

great! similar as kernel and image of homophrism

[BobBeatski]

I can't explain why I find matrices so exciting.