The Gram-Schmidt Process

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The Gram-Schmidt Process

Рет қаралды 308,239

Күн бұрын

We know about orthogonal vectors, and we know how to generate an orthonormal basis for a vector space given some orthogonal basis. But how do we generate an orthogonal or orthonormal basis given some other basis comprised of vectors that are not orthogonal? We can use the Gram-Schmidt Process! It looks tricky at first glance, but it's not too bad. Let's give it a try!
Script by Howard Whittle
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Пікірлер: 143

@omyrazeem2571 4 жыл бұрын

This 10 minute explanation is better than 2 hour lecture in class.

@nkwdtwg1352 3 жыл бұрын

People who say things like you do just don't understand how to teach. Teaching in a class and teaching on KZfaq are fundamentally two different things.

@holyshit922 3 жыл бұрын

I agree that it is explained well In my opinion decomposition the vector into its components could be the introduce to this method (decomposition the vector into its components is for Gram Schmidt like searching max for sorting)

@nathanjeong 2 жыл бұрын

@@nkwdtwg1352 how so? 🧐

@Vishal-by3vr 2 жыл бұрын

So true

@asmundhommepaulsen945 2 жыл бұрын

Legit

@brownviking8609 3 жыл бұрын

Saw you destroy flat earthers earlier in the year and now when I’m taking linear algebra in university, you come through for me again. Great vid!!

@vizviz72405 Жыл бұрын

😂

@jessicapeng6270 4 жыл бұрын

Looked through several videos describing Gram-Schmidt and this was the most clear, thank you!

@blockchaineenthusiast3932 2 жыл бұрын

hello lovely Jessica , I like to conversesion with you

@anonymous9217w2 Жыл бұрын

@@blockchaineenthusiast3932 lol

@bioscience6320 2 жыл бұрын

I really, appreciate your way of presentation ( short, precise and to the point). I never understand my lectures without you. Thanks a lot professor Dave.

@maxxie878 5 жыл бұрын

Wow. I love it. It's easy to get mixed up when you're using it, so it's great so see this explained in simple steps.

@swaroopsalvi47 Жыл бұрын

Thanks, looked several videos on this but your explanation is the simplest.❤

@AkhtarMehraj 10 ай бұрын

Best explanation I saw on KZfaq. Keep uploading such useful content. Thank You.

@user-rx1rr6hk7d 7 ай бұрын

I really have to thank you. I discovered your channel in my junior year when I went abroad to the US and studied Physics 1, when I already studied Physics 3 in Italy, my homeland. Obviously, your videos were very basic because the content was such. I'm now in my freshman year in university, and have rediscovered your channel through these videos about linear algebra and calculus BC, and am really glad I did, you have helped me a lot. My partial went amazing, all exercises were flawless (although I have to study theorems better), and it's also thanks to you :)

@BlackCat-ov4tc Жыл бұрын

I loved how the explanation is so simple and clear, thank you professor :)

@abnerandreymartinezzamudio3366 2 жыл бұрын

Simplicity is a great demonstration of genius. Thank you!

@YTjugal 4 жыл бұрын

Best, easiest & most visual explanation of the Gram-Schmidt Process. Thank you Professor Dave :)

@Atlas_Enderium 3 жыл бұрын

your videos are saving me hours of studying time for my upcoming Linear Algebra exams 😭 thank you

@braydenchan138 Жыл бұрын

Prof. Dave is a genius in education. We NEED you!

@mirai8274 3 ай бұрын

Thanks a bunch! Short and well explained.

@vaibhavkhobragade9773 3 жыл бұрын

Terse and concise explanation! Thank you

@ekleanthony7997 3 жыл бұрын

this video is super helpful... thank you professor for your awesome explanation

@Lila-lc7wd 4 жыл бұрын

Thanks a lot for this series!!

@ditya3548 2 жыл бұрын

This has been really helpful to me. Thank you very much

@tiodharmawan4905 Жыл бұрын

Many thanks Professor Dave, it is very helpful

@pugazhmathi.r3133 3 жыл бұрын

I haven't never seen the lecture like this.....awesome..

@enthusiasticsimple901 2 жыл бұрын

Great explanation... Much better than my 1hr college class. Keep Going🔥🔥❤

@aminaahmed1997 Жыл бұрын

High five Prof Dave. Thanks to u now am all set for my exam tomorrow 😊

@arty7926 2 жыл бұрын

Had to implement it in python, was very easy thanks to your tutorial!

@kasra-ir5io 8 ай бұрын

bro in just one day I finished more than 20 hours lecture just by using your videos. thank alot man you saved me ❤

@sujitkale7808 Жыл бұрын

Very nicely explained sir thank you so much❤

@bobbykuhikar5527 3 жыл бұрын

best and awesome explanation!!

@aviadlampert5956 Жыл бұрын

These videos save me. Thank you!

@Youngballer739 5 ай бұрын

Great explanation man

@reamabdulsalam524 8 ай бұрын

Hi thanks Dave really you made my life much easier you don’t know how long I have spent on this topic online to understand! Hours and weeks with no any benefit but with your 10 minutes explains it was really easy and now I can understand it should my Dr in university watch your clip thanks please do explain as well how to get the projection matrix onto a line ax=-by thanks

@sugandhm2666 2 жыл бұрын

Crystal clear explaination

@KM-di8zl 3 жыл бұрын

You sir, are a LEGEND !

@browniesnofrownies4843 2 жыл бұрын

Thank you so much for this

@tomatrix7525 4 жыл бұрын

At 4:12, to get tye length of the vector, don’t we need to sq rt. the dot product? On your illustration I only see you performing the dot product operation without the root...Am I missunderstanding something? Edit: noticed thr square outisde the vector length, thus undoing the root. Makes sense now. Sorry about that silly question

@AK-lu8ml 11 ай бұрын

simple and clear..👍

@bhattialdo3208 5 жыл бұрын

Sir you are very understanding. Keep it up.

@omyrazeem2571 4 жыл бұрын

great explanation ...

@akosdanielbollok4956 2 жыл бұрын

In the comprehension, no matter what I do, as an orthogonal vector I always get [10/3 5/2 10/3] and when I divide it by it's length I get a totally different answer... what could I have been soing wrong?

@user-be3jx1xd1w 4 ай бұрын

Do the calculations again, You'll get it. Here is the answer: So you get the orthogonal vector as [10/3 5/3 10/3]. You take out 5/3 as common from the orthogonal vector, you get 5/3*[2 1 2]. Calculate the length of this vector, you get √(10/3*10/3 + 5/3*5/3 + 10/3*10/3) = √(225/9) = 15/3. Then finding the orthonormal vector i.e., u2/(length of u2). (1 / (15/3) ) * 5/3*[2 1 2] = 3/15 * 5/3 * the vector which results 1/3 * [ 2 1 2] which also can be written as [ 2/3 1/3 2/3] . I hope you understood this and this would have helped you!!

@trashpanda70 3 жыл бұрын

An amazing and clear breakdown of the process, thank you so much

@chamithdilshan3547 2 жыл бұрын

Thank you so much!

@DeliriumzzZ 2 ай бұрын

My wrist is numb just from working through both problems, but I understand it. Thanks Dave! I will send the physio bill shortly.

@gauravsaxena7075 3 жыл бұрын

dude explanation is excellent

@erinmeyers-t9w 4 ай бұрын

thanks professor dave!

@sankhadas1080 Жыл бұрын

Thanku sir....its soo helpful

@novinnouri764 2 жыл бұрын

thanks for this video

@alaadusokey262 2 жыл бұрын

great content, thnx

@dgormley 2 жыл бұрын

I'm paying $7k for the class I'm in but this is free and much clearer. Life is strange.

@brianzhu4221 8 ай бұрын

Dave is just that guy, he is that guy

@transfo47 4 жыл бұрын

Excellent as always Dave.

@RahulSharma-oc2qd 3 жыл бұрын

Can we say that original basis and orthonormal basis, both can be shown as linear combination of the other? if I consider {e1,e2,...en) as the orthonormal basis of the vector space V and {g1,g2....gn} original basis of the vector space, then ei= Einstein summation(scalar).gi (where i=1,2....n)? Am I missing something at 4:10?

@funnysareen 4 жыл бұрын

You are a beast! Thank you Prof!! Differential Equation section next??

@ProfessorDaveExplains 4 жыл бұрын

Yes as soon as I find someone who can write the scripts!

@funnysareen 4 жыл бұрын

@@ProfessorDaveExplains Can't wait !!

@navagharkiran5769 4 жыл бұрын

sir, will u make vidoes about Real Analysis , since its complicated in maths.. i Know u will explain it better to us plz . a lot of Indians not understand it due to lack of correct explaination in college

@user-fz2df2gj4r 6 ай бұрын

thx you saved my life

@holyshit922 3 жыл бұрын

Good for pencil and paper calculations but i need better procedure if i want to write program for orthogononalization because of numerical reasons

@ryanjackson0x 2 жыл бұрын

Isn't dividing by the (total) length of a vector only one way of normalizing a vector? How you should do it depends on the norm you are using, is my understanding.

@payaparapasu Жыл бұрын

thank you very much

@reywilli8892 3 жыл бұрын

Thank you so much from Berkeley grad student

@thegeekypai Жыл бұрын

Thank you😍

@GAMIDATA 3 жыл бұрын

very much useful

@abdullahyto 6 ай бұрын

Thanks dude

@bouyancyyang943 2 жыл бұрын

what is the expression for orthonormal basis? just orthogonal basis/length?

@sachinrajpandey5242 Жыл бұрын

I am getting different answer for u3 for the question asked in checking comprehension, will you please tell me I am right or wrong. I tried a lot but my answer is different, for u3, from that given in the video.

@daveleung8081 2 жыл бұрын

this guy deserve more views

@manishverma6135 3 жыл бұрын

Thank You.

@Jehannum2000 4 жыл бұрын

At first I couldn't understand how you could just remove bits of vectors willy-nilly (ad hoc). I then realised that these are not equations where if you take something off one side you have to add it to the other side - they're definitions of new vectors.

@eittorres 3 жыл бұрын

Can you do a playlist on statistics? Thank you for time and effort.

@averywilliams2140 3 жыл бұрын

The notation part in the definition you used a determinant notation '|u|' for the norm instead of the ||u|| notation. Just posted for edification. Good video also.

@iamrising7176 2 жыл бұрын

This is sooo amazing. Thanks buddy. I would love to join the channel but my local card ain't accepted.

@darcash1738 4 ай бұрын

is there dot prod mult for TI-84?

@mcqnpc Жыл бұрын

hello, what if i have 2 vectors that are perpendicular but one is not?

@AsadKhan-ki2in 2 жыл бұрын

Real professor 🌺

@PetBuddies Жыл бұрын

Is the answer provided for the exercise correct?

@user-tn8zn3iz8u 14 күн бұрын

what does it mean for vectors to be orthogonal?

@mohammadidreesbhat1109 Жыл бұрын

Sir, great. They teach only evaluation in class

@srinjoydeyofficial 3 ай бұрын

Thanks

@nuwagabaedgar6580 2 жыл бұрын

Am sure it will also help me figure out

@vickysingh-hm5rf Жыл бұрын

Thenx

@RadoHudran 2 жыл бұрын

nice cut

@randymartin5500 2 жыл бұрын

At 10:06, U2 1st component and 3rd component is not coming out as 1/√6. I get 1/3*√3/√2 = √6/6 .

@willjohnston2959 2 жыл бұрын

√6/6 is same as 1/√6 so either answer is okay. Prove the ratios are equivalent using cross products, or multiply second fraction by √6/√6 to get first one.

@wijnand4762 2 жыл бұрын

thanxs

@ryanjackson0x 2 жыл бұрын

Are the starting basis vectors assumed to be sorted by magnitude? If not, does that mean v1 is arbitrary?

@luminousvalentine8011 Жыл бұрын

I guess so

@lochansanju6757 Жыл бұрын

Bro how did u take u1. U1=3

@Rajath_2001 2 жыл бұрын

Why is it always that, i don't understand, no matter how hard I try, in class. But, understand it completely in a 10 min video ....

@srinityapadma5125 3 жыл бұрын

Thank you so much Sir.../\

@trashhollowknightplayer4199 2 ай бұрын

I think you just saved my exam 😂

@commandershepard1944 3 жыл бұрын

Shouldn't U3 be equal to (-1/2,0,-1/2)?

@luminousvalentine8011 Жыл бұрын

Yes they're the same

@DaanishPeerkhan 2 жыл бұрын

Damn I just studied this 15 minutes before my test and guess what I could solve it :)

@bouyancyyang943 2 жыл бұрын

answer at 9:33 is orthogonal basis not the final answer.

@nghiaducduong 3 жыл бұрын

Legend

@miminaechali7058 Жыл бұрын

Wowwwwww!! The procedure is that too simple

@glaizamenguita109 2 жыл бұрын

DO U HAVE THE SOFT COPY OF YOUR PRESENTATION?

@t_n_t_o6519 3 жыл бұрын

@Professor Dave Explains Shouldn't it be like that 5:23 -> (1 0 1)^T - 2/3 * (1 -1 1)^T = (1 0 1)^T - (-2/3 2/3 -2/3)^T = (5/3 -2/3 5/3)^T Because of the (-(2/3) * 1, (-2/3) * (-1) and (-2/3) * 1) -> (- & - equals + and - & + equals -) (I'm using the transpose of the the row vectors ^^ hope it is clear :D) It just confused me a little bit but else I love your videos seriously I'm a CS student and those videos of yours are better then my lectures!!