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!
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.
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!
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
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.
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!
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
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.
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!
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.
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).
