Orthogonal complements | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

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Orthogonal Complements as subspaces.
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[@twonulator]

For those complaining that these videos contain too many proof style lectures, it is because they are intended for university level instruction where proofs are required comprehension.

[@rubanpillay]

twonulator true. I got this topic in a test tomorrow and it alone has 19 proofs

[@tiabarber4312]

twonulator proofs help, but examples help the proofs "stick"

[@iLoveTurtlesHaha]

Also, they need not pay attention to those parts, if all they want is to do it, they can just take away those parts. Geez, people are so dumb sometimes.

[@edwalkcow8214]

with that being said, if we need proof style lectures, it already existed in the lecture notes. but we didn't understand the lecture, thats why we are here, we are looking for alternatives.

[@MadsWest]

Sal is the king of explaining maths to everybody in my book. Can't imagine how many individuals he has helped this way. Really nice with repetition of what elements in the transposed matrix are dotted with what elements in the vector. I know this is very elementary, but for some reasong I find it hard to recall every time I'm calculating this manually and in terms of understanding what is actually happening behind the scene.

[@AsadAli-rd2mk]

This channel is way ahead of the current time

[@artema5535]

don't know why all people you keep blaming on sal's lecture. I thought this lec made a lot of sense to me and he did his job well. He does not prepare his lectures but does straight on the fly from his mind . so please respect that and do not say: " "uhmm write it like... lemme write it like"""... typical nonsense ignorance. If you don't like it, then skip it. There are tons of similar videos on this topic on youtube to watch.

[@rafiy7150]

agreed I still remember in my uni basic physics course the lecturer made me memorize all the formulas, then I decided to learn in khan academy and I dont really have to memorize anymore they just stick in my head because I know the analogy where they all come from

[@ibnsweeney]

why dont you do an example?

[@CoolDude911]

The 0 vector being in the set needs to be shown just to show the set is non-empty the first two properties hold for the empty set.

[@nils123007]

This video is nine Years old. Yet, it's more comprehensive and easier to understand than most lectures out there...

[@danishfella]

V perp, not for perpetrator, but for PERPENDICULAR!

[@VishyKc]

It's linear algebra. I study this in Croatia at the college right now and it is pretty awesome. Go to college of mathematics, you'll learn super interesting things. Programming is cool too ;)

[@BrotherOfHercules]

What u do now bro?

[@Barba_007]

quick recap : null space of (A) is the orthogonal complement of the subspace spanned by row elements of A (or subspace of colum elements of A transposed)... thank me later

[@anirudhkannan9]

Thank you

[@simaysokmen]

thanked 3 years later

[@AvivAtias]

@comecra85 In fact, as much as I know (weird terminology...) "these things", meaning the whole formalization and exploration of the algebra of the 1 and 2 dimensional mathematical objects: vectors & matrices consisting Linear Algebra, are the building blocks for "other things" investigated by natural sciences, which doubtlessly help to solve a wide variety of real life problems (consider the microwave). Anyway, whether you believe it or not, some people (like me) actually enjoy these inquiries.

[@davidk7212]

If you're searching KZbin specifically for how to compute/solve such things with no interest in the theory or the "proofy" aspects of it, you're wasting your time. You shouldn't even be taking whatever course you're taking because all you're going to "learn" is how to inefficiently do what Mathematica can do, and you'll forget it within a few months anyway. Even if this is just for some prerequisite you need, you need it for a reason and should take it seriously.

[@BrotherOfHercules]

You are the best teacher in the world.

[@wsmao1154]

it's very clear to understand why we have this property ! it's help and thanks for doing this ! really appreciate it !

[@terence321]

This is an excellent explanation and proof

[@hcsquad7357]

Can I download the board?

[@HoloUniverse]

Thank you!

[@jonathanjordan21]

9:45 I think it shouldnt be a transpose since its a dot product. vector X order is m x 1

[@user-wr6ek9fx1x]

10:14 that should be row-m?

[@Procuste34iOSh]

Yes

[@sohjunwen5490]

THANK YOU SAL!

[@gianlucacastro5281]

Sal once again bringing the knowledge we need

[@thelastcipher9135]

one tip. always have a pen and paper beside to use and rewatch over and over til everything sinks in - don't give up

[@mahlejas]

it is not so important but at 10:26 Rn sould be that Rm. FYI. Thanks for your videos they are so helpful.

[@grimmovers]

thnx

[@user-kj8kq7tf1q]

linear algebra is very difficult

[@TheBetterGamer]

Hey did you know you can have 4 orthogonal lines? It's possible. Go ahead, think about it for a bit.

[@SpotlessWanderer]

x=y=z, x=-y=z, -x=y=z and -x=-y=z ? For example..

[@kanamei9170]

Both Chinese subtitles are wrong. please fix it.

[@FungwaaTongwan]

still wrong now 复制粘贴什么玩意QAQ

[@astinmartindriver]

Too proofy.

[@Barba_007]

same notation for row and col spaces dude, you can easily get lost here

[@sirfalcon1]

Way too proofy. I just need to know how to find the orthogonal complement. Do an example or something.

[@landonbarnett4865]

+Lord Falcon It appears to be aimed at university level, since proof is important when trying to truly understand something. If you just need examples, look for lower level videos...

[@DarknessIsThePath]

Except proofs barely mean shit on exams.

[@tordurhansen333]

Depends on the exam. We prove loads of stuff where I'm attenting, even in exams.

[@landonbarnett4865]

Tordur Hansen I agree, here in Italy 50% of the exam is oral in which only theory and proofs are asked.

[@jonaskatona7136]

Proofs are essential (and usually required) in more advanced math courses. Even in the first linear algebra course at my university, on both of our ten-question midterms, two or three of the questions were proofs. In the second, more advanced one, it's ~80% proofs.

[@keremkurban8156]

Even though being 22 mins of video, its only equivalent to less than 11 minutes since everyting is repeated more than twice. Annoying!! But thx for effort

[@Soymilllk]

i dont like the new writing style! i miss the cool old pixelated numbers and diagrams!

[@erithug]

very lame joke he said!

[@Krazyerd]

Getting seriously annoyed by the "uhhm lemme write it like.. lemme write it like...". Literally took up 5 minutes of the video.

[@cha81153]

BORING!

[@hossamarafa705]

what a waste of time