Vector triangle inequality | Vectors and spaces | Linear Algebra

Vector triangle inequality | Vectors and spaces | Linear Algebra | Khan Academy

Рет қаралды 244,200

Күн бұрын

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Proving the triangle inequality for vectors in Rn
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Пікірлер: 28

@The.Ghost.of.Tom.Joad. 12 жыл бұрын

Thanks Sal. You are a great teacher. Twenty or so years ago, the Cauchy-Schwarz and Triangle inequalities baffled me. I never understood them--just parroted some worked examples I had. Compare. ->You: I listen and jot some things down for 25 minutes. My understanding, solid. I pulled out an old LA book, and ripped off a few problems correctly. No need to look @ the solved problems. ->OSU ~1990: 3 lecture, 5 recitation and over 10 study hours. Baffled. Had to memorize algorithms. Thanks

@thecubemaster 13 жыл бұрын

Hard concepts + Sal = enlightenment

@LAnonHubbard 13 жыл бұрын

This was really helpful to see what the previous video was meaning. Thanks.

@panickingkiwi943 3 жыл бұрын

11 years later, still of great help. Thank you hahahah.

@JaspreetSingh-zp2nm 4 жыл бұрын

Sal, What argument would you use to prove triangle inequality for vectors that are not colinear? Or when y is not some scalar multiple of x.

@hafsamariyam7176 Ай бұрын

That could be a great video if some corrections were made. 1. In the first step, that is, length squared of x+y doesn't equal the dot product of vector with itself; dot product should be replaced with sum of the vectors.

@bumblebeee5 14 жыл бұрын

this writing is so clear

@rbud7 11 жыл бұрын

Thank you for this. :)

@faulty_sebastian_ 7 жыл бұрын

this is cool

@regingwapo 14 жыл бұрын

I think it would be more insightful if you provide a geometric interpretation of x=cy at 14:50

@virtualgirl1162 4 жыл бұрын

Thanku very much

@shuvashishsharma1299 Жыл бұрын

Thanks boss

@PhysicsMath 5 жыл бұрын

Prove vectorially that the opposite side of parallelogram are equal and diagonals bisect each other

@annerigouws5063 7 жыл бұрын

How can I use this result ||x + y||

@Liaomiao 11 жыл бұрын

lol @ nerd rage in the comments, kinda lightens the mood from all this concentration

@souravmallick7699 3 жыл бұрын

Just here after 11 year's to solve my present problem 😶

@eileenBrain 13 жыл бұрын

@Hefotos ok apart from triangle inequality, but still not enough examples and explanations in 3d space. it would be better if the tutorials were more about 3d space oriented and not algebra equation solving and simplifying something that is simple enough.

@LordOfNoobstown 3 жыл бұрын

it does not matter, the vectors could as well be in 3d space

@DTNRom88 14 жыл бұрын

@xiewenyi his head

@saggre 7 жыл бұрын

@mumcarpet109 6 жыл бұрын

TTD

@mumcarpet109 6 жыл бұрын

Vector Andy

@boomit666 11 жыл бұрын

He prolly wasn't gonna pass the test anyway , hence even this explanation was too hard for him to comprehend :D

@fredirecko 4 жыл бұрын

He kept saying magnitude.....it drove me crazy😂

@Technium 4 жыл бұрын

Cowshie Shorts

@eileenBrain 13 жыл бұрын

Ok so i guess the audience is him himself! Otherwise why would anyone waste their time watching this crap when they can simply look things in some book?! Which would be better and quicker. Thought this stuff was for beginners, but this guy goes on about some meaningless examples like two vectors and solves meaningless equations with them. So my point is, if you want to apply this to a meaningful example with a 3d graphics api then you are left with nothing helpful at this moment.

@Akash-ht1mq Жыл бұрын

I dont think your gonna say the same thing now looking at 235k views. Lmao