Gram-Schmidt Orthogonalization

[@neevetiasli]

I have a disease, i can't learn something before understanding the logic behind it. Now thanks to you sir, i am learning this processus and never forgetting it!

[@mostofatanvir595]

same disease

[@neevetiasli]

@mostofatanvir595 i'd say get well soon but i know it's incurable

[@joshstephenson9711]

There are hundreds of videos about Gram-Schmidt, but this is the best one that demonstrates it visually, which is imperative to understanding it intuitively. Thanks!

[@amardeep0812]

Dear sir... I have been trying to learn this process through books for past week..... but there's no explanation in any book or on Internet that could actually match this. this visual description has clear all my doubts thank you so much... lots of love from India.

[@rolloisles]

Glad it was helpful! Thank you.

[@johnbrownell1]

Thanks for actually showing this instead of just assuming that this literally just plays out perfectly in everyones head. I don't understand how people think linear algebra should be taught with just a chalkboard in 2019

[@dangries3868]

It certainly didn't play out perfectly in my head when I first learned it! I'm still using plenty of chalk in the classroom but it sure is nice to have some technology to make this easier to understand.

[@afsinyilmaz8665]

I was struggling to understand the reason behind subtracting one additional term for each additional base vector to remove parts that are not orthogonal with Gram-Schmidt and this visual did it for me. Great!

[@grooveseeker6269]

THANK YOU! I couldn't gasp why subtracting the proyecting would give you the desired vector, thank you sooo much

[@MegaAlindo]

Brilliant geometric explanation. Nowhere in youtube I was able to find something like this where I can visualize what I am doing. Thank you so much and I would hope that you make more videos like this

[@dangries3868]

Thanks! Glad it was helpful.

[@akanguven114]

In every time span may God bless you! Thanks

[@deakinsrbut]

Great explanation. I can get the math anywhere, but your visual explanation is the best I've seen so far. Do more videos!!! :D

[@rmodur]

Wonderful explanation, this is the best video on this topic. Thank you!

[@vicen1090]

This, the most clear, visualy appealing and well define representation! Ty ty

[@olayinkajosiahajayi8330]

Thank you Dan. This explanation is beautiful.

[@sanjaisrao484]

thanks for the excellent explanation You are great , keep helping people

[@LawrenceChan-me1rw]

Excellent interpretation and explanation of the process. Very intuitive!

[@loganynguyen]

Way more clear and concise than anyone else. Thanks!

[@isxp]

Excellent explanation. I wish I was never told that the standard vector basis were always perpendicular and of length one, because now I've had such a difficult time learning about basis, vector spaces, and inner products, because I kept thinking they needed to be perpendicular the way i, j, k are. Hearing you say "these two basis vectors may not be perpendicular or of length one" was like the moment where it all clicked.

[@ulumaika1455]

Can't express how much I appreciate the visual representation! Taking linear algebra for the first time has proved difficult in the realm of trying to visualize whats actually going on in the mess of notation and mathy proof readings. But your video explains it perfectly! You definitely deserve more views on this. Keep up the good work my guy and much aloha from out here in the 808!

[@rolloisles]

ʻUlu Maika Thank you! This was something I put together mainly for my students, but I'm very glad you also found it useful!

[@IanRichardArko]

This was amazing! Thank you for making it all so clear :)

[@yeast4529]

Thanks, really helpful to understand the visual representation amongst of all the written work

[@the_l0st317]

Exactly what i was looking for, Mr. 3B1B jr.

[@jaisejohnson]

Wow that was a great explanation ,thank you.

[@samihahsharif7441]

That was amazing, sir!

[@최경훈-w5y]

이해하기 쉽네요. 좋은 강의 고맙습니다. its easy to understand. thank for such a good lecture

[@stanbaltazar]

That was a great visualization. Thank you!

[@filippodembech7659]

Thanks to have explained this process so well!

[@davidfield5295]

Great explanation

[@haiderrizvi7927]

Thank you so much I m literally crying!

[@jacobzetterfeldt3652]

great explanation. Thank you for the help :)

[@chessmaster6407]

Excellent! Very clear explanation

[@matansavage]

wow. great explanation. thanks

[@Sipnayan]

Excellent video. Thank you.

[@eyton8558]

This is a great video thank you

[@pujachakraborty8163]

It is great ... and itz vey amenable to understand.. thanks... actually i was seeking for this type of pictorial view

[@JannisAdmek]

thanks so much! I really like the intuitive explanation!

[@ProduccionesLukaz]

Great video! Please let me add subtitles to this so I can share it with more people :D

[@durumbasa]

Wow man, thank you so much! God bless you.

[@AnonymousIguana]

Great, thanks :D. I love internet for such a good quality education materials :)

[@timothyryan8753]

This helped a little bit but man is this stuff hard to grasp. Definitely gonna fck this up on the test.

[@jonahperelman5175]

goated video, cheers!

[@fionazengyuqi1746]

Thanks sirrrrr helped a lot!

[@alanmichaelthayil967]

Thank you very much for this video :)

[@rosenasena2630]

Thank you so much sir... it helped alot!

[@groenekool]

Thank you for the explanation!

[@harshitkatiyar3901]

Thanks this is much helpful

[@johnstone6848]

Well illustrated thanks a lot. What software did you use to make the purple plane at the beginning? I really need to get something like that for my linear algebra class.

[@rolloisles]

Geogebra. It's free! Sorry, I should have mentioned that somewhere.

[@asylantragqled4270]

Incredible

[@k12classesbyrahulsir30]

Awesome sir

[@zumrazen]

I can't explain that how helpful it is! More, please :) Thanks a lot. I'd like to ask which programme did you use for this animation, professor?

[@dangries3868]

Glad you found it helpful! I used Geogebra for the plots, and Screencast-o-matic to capture the video.

[@bensas42]

THANK YOU!

[@slaozeren8742]

thank you, sir!

[@ycombinator765]

Beautiful

[@zuherkhalaf2679]

Which Programm do you use for this visualisation if I may ask ?

[@tuongnguyen9391]

Hey what kind of software that enable you to do that ?

[@00incog00]

Thank you so much

[@madeleinesong2418]

Hello, what visualization software is this?

[@faazabidi]

Excellent

[@dystopian_1]

Wow... thanks a ton

[@ejjoxe6594]

THANK YOU

[@svenzanetti5637]

Perfect!

[@stevenmoore4947]

Awesome job! What visualization tool are you using?

[@dangries3868]

Thank you. I used Geogebra. You can do a lot with it!

[@himanshuchauhan9865]

crystal clear

[@eboyofcolour945]

this is amazing lol

[@koala1578]

ily

[@mahmoudmaher00]

Will it be: (-11/10, 33/10)?

[@dangries3868]

That's pointing in the right direction for the second vector, but don't forget to normalize. The two vectors are 1/sqrt(10)(3, 1) and 1/sqrt(10)(-1, 3).

[@dbf72829]

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