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

Orthogonal Complements as subspaces.

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[jaydean]

I don't know if your listeners are aware of how much work and time you put into doing these videos, but THANK YOU- the BEST teachers are the ones who UNDERTAND the material that they teach THANK YOU

[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.

[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.

[AsadAli-rdmk]

This channel is way ahead of the current time

[artema]

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. 

[nils]

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

[CoolDude]

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.

[Barba_]

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

[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 ;)

[davidk]

If you're searching Youtube 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.

[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.

[danishfella]

V perp, not for perpetrator, but for PERPENDICULAR!

[wsmao]

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

[BrotherOfHercules]

You are the best teacher in the world.

[gianlucacastro]

Sal once again bringing the knowledge we need

[othi-kk]

This is an excellent explanation and proof

[jonathanjordan]

9:45

I think it shouldnt be a transpose since its a dot product.

vector X order is m x 1

[thelastcipher]

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.

[TheBetterGamer]

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