Linear Algebra 19a: Component Spaces - What They Are for and When to Use Them

bit.ly/PavelPa...
lem.ma/LA - Linear Algebra on Lemma
bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook
lem.ma/prep - Complete SAT Math Prep

[@MathTheBeautiful]

Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

[@huidezhu7566]

Really the best Linear Algebra videos on the internet. I love these so much

[@abc123634]

It's almost the end of 2019 but this video is still so inspiring, related and insightful. It's not how many views, its how many memories. Thank you, professor.

[@albertlee9592]

Your airplane vs car analogy is a life lesson that will go a long way. Thank you!!!

[@gimmemoreborisbrejcha9794]

This video is one of the examples, why these series feels like an actual university course. Not only the formulas and techniques, but the actual intuitions are also provided.

[@MathTheBeautiful]

Check out lem.ma/LA1 - it's an actual actual university course.

[@gimmemoreborisbrejcha9794]

@@MathTheBeautiful pardon me, I could not find a name of a university in the link. Is that something like a virtual university?

[@MichelCarroll]

Love your explanations and analogies. Your channel is a gold mine. Cheers!

[@synuk5712]

it is so sad that there are only 1724 views and any celebrity reach millions. thank you for your videos.

[@MathTheBeautiful]

Hi Miguel, thanks for your comment. When I complained about this to Gilbert Strang, he told me "It's not how many views, it's how many memories."

[@mohammedal-haddad2652]

It is a small club.

[@aufderpapenburg]

Noise could sometimes be much louder than signal. Despite this fact, signal is always much more meaningful than noise.

[@profesorius78]

I think low number of views may be partly because of the first playlist. First playlist is too long and dragging. While establishing strong foundation is important, imo it could be done in a more compact way. 20 hours of lectures just to arrive to Gaussian Elimination and Inverses is too much (Strang manages to do the whole course in a similar amount of hours). And it is difficult to skip, because it constantly feels some important point should arrive soon in next video. Then in next video, then in next... It's difficult to survive first playlist, but such a relief to arrive at this one :)

[@rd-tk6js]

Lucidly explained ! Thanks !

[@danv8718]

And happy 2019 too!! May you never stop posting videos. Your channel is a real treasure.

[@mohammedal-haddad2652]

I always prefer these philosophical explanations over hardcore equations. Thank you very much.

[@MathTheBeautiful]

Me too!

[@boutiquemaths]

I didn't know where that metaphor of the plane trip was going but when it finally landed I was laughing. A powerful metaphor we are unlikely to forget! Second to the wine tasting one, that was the best.

[@HKExperimentalman]

Happy New Year ~ Thanks for your many nice lectures ~

[@nimaisarkar3786]

thanks a lot for this lecture along with that example .it was realy helpfull to understand the concept

[@avneel]

"So soon, it will sound like such a long time ago."
True words, I can't believe 2015 was almost a decade ago.

[@oleksandrkhomandyak3860]

indeed it's 2024

[@luisribeiro2239]

very nice insite. Thank you very much for your wok.

[@MathTheBeautiful]

Hi Luis, thank you for your nice comment! Made ma hungry for stir fry.

[@richardaversa7128]

Happy 2015!

[@isurujanith3146]

0:01 2021 Not so happy though 🤒🤒

[@philblandford5560]

Enjoy 2015, it's downhill from there

[@MathTheBeautiful]

I have hope!