Gram-Schmidt example with 3 basis vectors | Linear Algebra

Gram-Schmidt example with 3 basis vectors | Linear Algebra | Khan Academy

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@dominicpotter1 13 жыл бұрын

I just had one of those "eureka!" moments where everything finally clicked and I understood it all. My exam's in two days, so it's just in time. Thank you so much :D

@theBIGamazingShim 14 жыл бұрын

have you done a QR facorization video? if not could you :D it would be helpful.

@blondii0072 13 жыл бұрын

Thanks alot, i just found the video so easy to follow. You rock

@nicolasseifert 14 жыл бұрын

Thank you, i followed ur steps to do my webwork question :-)

@TheresaOtti1 13 жыл бұрын

Great! :-) I finally got that and we had like 3 examples for it in the Uni! This was a really good explanation! Haven't found one like that before!

@nnnames 12 жыл бұрын

Thank you soo much, this saved my evening! Really thank you!!

@elizabethk28 15 жыл бұрын

Thank you so much for taking the time to explain this, I am having a final in a couple of days and this is helping!

@Dan-bg5fm 7 жыл бұрын

elizabethk28 did you pass?

@SHONSL 9 жыл бұрын

Very instructive video, you've saved my life! Kudos.

@Endbringer534 8 жыл бұрын

Thanks, great introduction to GS orthogonalisation :)

@shadisc 13 жыл бұрын

what template are u using? looks great!

@ezrakim1323 2 жыл бұрын

Superb Explanation. But there's a calculation mistake on 5:58. Instead of ((3)^1/2)/2, you wrote (3/2)^1/2. So your entire calcualations of y3 was all wrong. But at least you made the concept very clear.

@danieletagliaferri8496 6 ай бұрын

there's no mistake there, sqrt(3/2) is the correct calculation for the length of y2.

@samanthatotalyrules 13 жыл бұрын

thank you so much for your video's! they have helped me out alot! much appreciated!

@ElifArslan-l9g 2 жыл бұрын

thank you

@Iphone-bk2mk 7 жыл бұрын

THANKS!

@dazzaondmic 6 жыл бұрын

I was under the impression that for a projection you divide by the norm squared. How come he doesn't do that? He just takes a scalar multiple of the vector where the scalar is the dot product. Has it got something to do with the fact that he normalises the vector beforehand?

@rfmvoers 6 жыл бұрын

Yes. Normally the projection of vector u on v would be ( u.v / v.v ) v , but if v has length 1, then v.v = 1, so you can write the projection as ( u.v ) v .

@MrHouse1337 10 жыл бұрын

Thanks! Ur awesome :)

@persinitrix 7 жыл бұрын

if v1 and v3 are already orthogonal wouldn't it be faster to only alter v2 by subtracting the projections v2 has on the other two vectors from the v2 vector??

@sukhlegend2614 11 жыл бұрын

flawless

@theodor320 7 жыл бұрын

Wouldn't it be neater to just multiply y2 with 2 so you would have a much cleaner vector u2? Or is that not allowed?

@brandonxu9278 7 жыл бұрын

shouldn't the projection of v2 onto v1 equate to the dot product of v2 & v1 divided by the magnitude squared, multiplied by some scalar, the emphasis of the magnitude being squared?

@adamjoyce8764 6 жыл бұрын

The dot product of the same unit vector is 1. So it doesn’t really matter.