Gram-Schmidt process example | Lecture 20 | Matrix Algebra for Engineers

[@ProfJeffreyChasnov]

Find other Matrix Algebra videos in my playlist th-cam.com/play/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx.html

[@alevelsos]

Thanks for your videos, I dont know if I passed but I was certainly able to write something on my paper today

[@davidcamposbrandao2215]

Thank you !! Very helpful and straight forward

[@jansenkosasih]

When normalizing u2, do you simply ignore 1/3?

[@ProfJeffreyChasnov]

Yes, can normalize all the vectors at the end.

[@professorhugo1468]

@@ProfJeffreyChasnov Sorry, I dont understand why .

[@weisanpang7173]

+professorhugo1468, normalizing a vector means making a vector of unit length (length=1) pointing in the same direction of the vector being normalized. Eg, given a vector (-2,1,1), there are infinite number of vectors that point in the same direction, eg. 2 x (-2,1,1), 3.5 x (-2,1,1), 12 x (-2,1,1), 0.15 x (-2,1,1)...etc, generalized to A x (-2,1,1), A being a variable. For all these set of vectors, the unit vector or vector of unit length is the same, that's 1/(length of (-2,1,1)) x (-2,1,1) = 1/sqrt(6) x (-2,1,1). Note, there's only 1 unit vector in any direction, it's unique.
It's the same as normalizing (-2A, 1A, 1A) => 1/sqrt[AxA(2x2 + 1x1 + 1x1)] x (-2A,1A,1A) => 1/(A x sqrt(6)) x (-2A,1A,1A) => bring 1/A into the vector, it will result in the same unit vector of 1/sqrt(6) x (-2,1,1).

[@kerrynhyde1254]

@ProfJeffreyChasnov sorry I just can't understand how normalising is derived from this equation "the unit vector or vector of unit length is the same, that's 1/(length of (-2,1,1)) x (-2,1,1)". Is it possible to have a dedicated video to show why that formula is used to obtain a normalised vector?

[@Alfonzo6000000]

Thank you!

[@aidalf1912]

thank you man

[@LucasChan-qd8gr]

Thank you !!!

[@sn1zy935]

genius