Gram-Schmidt Orthogonalization

The Gram-Schmidt Orthogonalization process can be used to find an orthonormal basis for a vector space, given any basis to start with.

[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!

[joshstephenson]

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!

[amardeep]

Dear sir... I have been trying to learn this process through books for past 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.

[DatVuongQuoc-rl]

i'm so thankful for your video, i don't know people can learn Linear Algebra without visual representation, thank you so much.

[johnbrownell]

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

[grooveseeker]

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

[afsinyilmaz]

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!

[akanguven]

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!

[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

[vicen]

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

[sanjaisrao]

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

[ulumaika]

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!

[loganynguyen]

Way more clear and concise than anyone else. Thanks!

[olayinkajosiahajayi]

Thank you Dan. This explanation is beautiful.

[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.

[LawrenceChan-merw]

Excellent interpretation and explanation of the process. Very intuitive!

[IanRichardArko]

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

[the_lst]

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