Gram-Schmidt Orthogonalization | MIT 18.06SC Linear Algebra, Fall 2011
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- Опубликовано: 13 окт 2024
- Gram-Schmidt Orthogonalization
Instructor: Ana Rita Pires
View the complete course: ocw.mit.edu/18-...
License: Creative Commons BY-NC-SA
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A feature of Prof. G. Strang's Linear Algebra is to treat a matrix as columns and matrix algebra simply as the combination of columns. This technique is vividly displayed in this tutorial. Concise, clear, insightful! No other word for MIT, just the best. And those 9-panel blackboards: the best instructional tool.
These recitations are such a great addition to the lectures. Simple but clear.
Wow she makes the process seem so easy and natural. Love it!
Every time I hit 'pause' I end up coming back a week later... Great instruction!
You literally just moved my grade from an B to an A in less that 5 minutes; I have been looking for this type of solution for hours on the internet. It would seem that only engineering institutions teach this method using column vectors. THANKS!!!!
This video was extremely helpful and clear in explaining how to perform the Gram-Schmidt orthogonalization for QR decomposition. The instructor demonstrated how to project vector b onto a and find the orthonormal vectors q1, q2, and q3. She also explained how to calculate the R matrix. The equation A = QR implies that the columns of A (a, b, c) can be expressed as a combination of the orthonormal vectors q1, q2, and q3. This fact was used to find the R matrix. This explanation was very well done and easy to follow. Thank you for this great lesson!
you have used a very smart approach to get the solution. It helped me a lot. Thank you, Maam.
I just love how you all teach using the 'bigger picture'. love ya all
As far as I understand it the projection of for example: b onto q1 is the dot product of b and q1 mutiplied by q1 itsself.
She's doing it in this video all the time, but the step of calling it the projection is just skipped and she goes straight to the part where its translated into dot(b,q1)*q1
You made me understand this in about 15 minutes whereas I couldn't after a whole semester in my native language!
Thanks very much!
I've got to say I'm still a bit confused how to produce the R-matrix when the matrix is not precomputed to get a Q matrix that does not consist of only integers.
This is awesome. I have revised for my exam with ease on this concept.
thank you very much.ı have an exam about this course.ı try to find a good source on internet but ı couldnt.hopefully ı saw thıs mıt course.ı learnt everything in a just 10 min.thank you again.god bless you!
You are the best given clasess... Now, I know how to applied the gram-schmidt method in matrix A =QR...thanks so much
Very easy examples professor. The problem that motivated me to watch this video has |q2'| = sqrt(3442)/7. Now deal with it and go for q3'. Arrrggghh
Thanx Ana you are amazing at the last minute.
Great, thank you for you have subtitled, because my English is not very good :)
thank you MIT!
U R DAMN GOOOOOOD!!! My linear algebra textbook describes it so complicated.
its better to follow Prof.Strand notation which says x = A' b / A'A, and B = b - xA
just before the exam. accurate recommend
thank you so much .
thanks
An excellent explanation. Thank you!
You just have saved my life!!!!... Thank you!!
Very good video! Thank you for posting, this makes perfect sense now.
Thanks so much for this ! It seems pretty easy now.
Thank you! After you explanation, everything has became very to me! :)
Very good.Not only the explanation but olso the Method are Excellent. :)
Thank you.
That's much more better than what my teacher taught!
Thank you very much!!!! That was such a beautiful explanation
this is 100...
exellent explanation
Thank you
thank you! Bless you!
Thank you for good lecture.
thannnnnnnk you so much！！！！！
do you know which speakers the instructor is using they are crisp clear like this lecture. thank you
thanks a lot!! from Turkey
wonderful lecture .
Thank you so much!!!
This was helpful. Thanks!
Beast mode.
great explaining. thanks
"Which Is, Well,.. Very Lucky... ;-P"
wow,this method is way better than mine.i got more easier and save more time by doing this method..tq damn much :)
THANKYOU SO MUCH!!!
Muy bueno, gracias
She reminds of the baby sitter from the first incredibles movie. Still, great video!
Great example.
She has a great accent
Excellent,
Can you say if the original 3 columns are linearly independent, then they span R3. Therefore we can just pick the easiest orthonormals spanning R3? ([1 0 0; 0 1 0; 0 0 1]?
A month later: since QR only works for square matrices (unless I remembered it wrong) and likely at university they will give you square matrices with linearly independent column vectors (otherwise we cannot perform QR decomposition), therefore Q will always be some sort of permutation matrix ?!
excellent
Please can you explain how did you find the lenghth is 1?
Let's say you have a vector v. You know that you can multiply v with any scalar k that it doesnt change v's direction. So, what you can do to find the unit vector on the direction of v is just multiply v with 1 / his lenght.
Who’s watching this during the COVID lockdown?
What do I do if my first vector is not (1,0,0) or (3,0,0) (where I just have to norm it) , but (1,0,1) and all the other vectors also don't just have one component? How do I get my first vector then?
+SWiSHRoyal Just as with (1,0,0) and (3,0,0), you can simply normalize (1,0,1) and use it as your first vector. When you're looking for a orthogonal basis for a space, the first vector you choose is arbitrary (as long as it's in the space, of course), since you can always find another vector in the space to which it is orthogonal.
why is length = 3 for q2? in @3:40
what's her way of getting the projection?
No likes the white line running across the board at 3:38.
very good thanks :)
0:51 NO!
thnx
merci
it was excellent but I m Turkish too
lol
dafuq rofl hahahah
I crack up when she walks away just to walk back 😂 what's the point? Just continue the lecture
Same man ahahaha
The video may be edited. God only knows whether she completed the video weeks after walking away.
wow
'bora Técnicoooooooooooo
this is legit witchcraft
u r a perfect teacher but I am Turkish
So?
Neme ?
What do you mean "but" you're turkish? What's the problem with that?
Neme I guess she wished the instruction was in turkish?
blurry video. couldn't MIT do any better?
Hey, 12 years old video. Keep in mind
@@o__bean__o 12 years ago is not 60 years ago. I have really sharp videos and movies that were made 60 years ago 😀
im left handed too.. :D
bayan sana helal olsun sonunda kafam bastı anasını satim
m chutiya hu
if im good at english, i can better understand math from english book.
Hi. i love u. bye
Thank you
thank you