I enjoy watching the super bowl and then coming here to see amazing catches in slow-motion. Noticing athleticism as a theme in these videos. Keep up the good work and sense of humor
There is a part about Lagrange in the video at 10:47, I couldn't understand clearly the idea mentioned there, is it a theorem? If it is, what is the name of the theorem? Thanks.
hi and thank you. as you've said - there are MANY possible def. for the INNER PRODUCT. You showed one example (for polyn.), the integral from -1 to 1. Under ALL POSSIBLE Inner Products this will hold? How do WE CHECK/PROVE without a SINGLE ONE DEF. of the Inner Product for Polyn. that (b1,a)=0 ? EDIT - The next Video Answers it :) Thanks anton
+MathTheBeautiful When you orthogonalize a vector or bunch of basis vectors in this way, aren't you changing its length and therefore getting only part of the "full picture?" Because each vector loses a piece of itself: the component that was parallel to the other vector. Is there another method to orthogonalize the basis vectors and still preserve their lengths?
Thanks for the amazing videos. Just a small correction, Algebra was named after al-Khwarizmi which was a Persian mathematician and astronomer not an Arab one! [ref: wiki !]
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
I enjoy watching the super bowl and then coming here to see amazing catches in slow-motion. Noticing athleticism as a theme in these videos. Keep up the good work and sense of humor
There is a part about Lagrange in the video at 10:47, I couldn't understand clearly the idea mentioned there, is it a theorem? If it is, what is the name of the theorem? Thanks.
hi and thank you. as you've said - there are MANY possible def. for the INNER PRODUCT. You showed one example (for polyn.), the integral from -1 to 1. Under ALL POSSIBLE Inner Products this will hold? How do WE CHECK/PROVE without a SINGLE ONE DEF. of the Inner Product for Polyn. that (b1,a)=0 ?
EDIT - The next Video Answers it :) Thanks
anton
👍
Cosmo Kramer co-discovered orthogonization of any basis along with Gram Schmidt.
It was a different Cosmo
How much of b, is made of a. "The b component of the vector a".
Well, Gram is an important mathematician. en.wikipedia.org/wiki/Gramian_matrix en.wikipedia.org/wiki/Metric_tensor
Thank you for your grt lecturer on QUANTUM MECHANICS 😂yeah am a physics student
+MathTheBeautiful When you orthogonalize a vector or bunch of basis vectors in this way, aren't you changing its length and therefore getting only part of the "full picture?" Because each vector loses a piece of itself: the component that was parallel to the other vector. Is there another method to orthogonalize the basis vectors and still preserve their lengths?
For finding alpha it should be divided by the square root of e.e, which is norm, not just e.e, which will give norm squared.
Agree. I was thinking the same.
6:02
Thanks for the amazing videos. Just a small correction, Algebra was named after al-Khwarizmi which was a Persian mathematician and astronomer not an Arab one! [ref: wiki !]
Mahdi Ghane he was arab
Well, now i don't feel that bad about calling it the Gram-Smith method 😪
Don't shit on Wikipedia, one of the only pure resources left in this world.
ahaha... Do you know how biased Wikipedia is on all matters that have to do with politics in some way?