### Linear Algebra: The Gram-Schmidt Process

by Khan Academy • 123,656 views

Finding an orthonormal basis for a subspace using the Gram-Schmidt Process More free lessons at: http://www.khanacademy.org/video?v=rHonltF77zI

As soon as I'm out of university and I get a job, I'm donating. I owe you so much Sal, thanks for all the help!
i've never understood this quite right at college but now as i take only this one 20 minute lecture at khanacademy i understand everything. thank you!!
damn your U :p Tutorials are really nice, and that's really helping. Thank you :)
You made small mistake, when you copied ( v3 u1 ) u1 + ( v3 u2 ) u2; you created "y3 = v3 - ( v3 u1 ) u1 + ( v3 u2 ) u2" right is, "y3 = v3 - ( v3 u1 ) u1 - ( v3 u2 ) u2", i think.
Explained so well! Thank you
Hm.. could someone please inform me if this is a correct conclusion: When he takes the dot product between (5min-10min) v_2 and u_1 and then multiplies by u_1 it's because the dot product yields the magnitude of the projection and by multiplying it with u_1 he gets the vector x? If this is the case; wouldn't it be the same thing to take dot product between v_2 and v_1 and then divide by |v_1| ?
Hes definitely right when he said its not that bad when youre dealing with the numbers. Memorize the equations and its not too bad. Understanding the proof and why is the hard part.
thanks
"Its that easy"...lol
For me, 20 minutes of this is worth more than a 2 hour lecture. Thank you!
Although my linear algebra instructor made this easy to follow in terms of the steps and calculations, watching this video I know actually understand WHAT we are doing when we perform these steps. Thank you Sal for the great video tutorial.
very hard...
Thanks kahn. You're really helpin me out with my math classes
Wish I could do the same. I don't go to many lectures but I still have to read my books because Khan Academy's math is not the kind of formal proof-oriented math you learn in pure mathematics
I...understand!
hey what program are you using for recording/writing up that stuff?
whosss the mann??? khansss the mannn
Haha you repeat things a lot, like individual words :)
I can't believe it, I'm starting to love Linear Algebra
these vids are great in conjunction with PAULS online math NOTES
Professor ~= Doctor ~= Moron
When I took Linear Algebra, I hit a wall with the gram-schmidt process. I could do the mechanical steps to orthonormalize a basis, however, I was having a hard time visualing what exactly was going on. After watching this video, it made perfect sense. In fact, Khan's whole playlist is worth watching. Linear Algebra is my favorite. <33333333
@sherajr me too lol
my prof tried to teach this in an hour ididnt get shit. i come here igot it in 5 minutes
'Orthogonal to these dudes'
On 5:00 you say V1 is not going to be on line spanned by U1. Actually it should be V2 and not V1 that is not going to be on line spanned by U1. Am i right? You are doing a great job. Keep it up :))
When i saw the title i was like: "I know Gram-Schmidt, it´s easy", when i finished the Video is was like: "Aaaaaaaaaah, thats how it works!"
Where can i find the bibliography you used for this lecture? Now I've got the idea but i'd like to read it ;/
i couldn't see any better reference for me to understand Linear Alg. other than these lecture!! saying thanks won't be enough!
@sherajr You must be in my class. I hate that lady.
i love you
@TheNef77 same story
thanks. well explained
Much appreciated!
I started clapping. :')
Thanks man
Best Explanation EVER!
Is there a video from khan that is about "inner product spaces"? Help would be greatly appreciated. Thanks!
Khan I am almost done with Linear Algebra and I am passing the class all thanks to your help. Most people can't believe I study math for fun and have no intention in going into any math intensive field, most math accountants need is watered down Calculus but I have finished Calculus 1,2,3 Physics 1 and 2, Linear Algebra, Differential Equations and its all because of my deep curiousity to understand nature at my own pace knowing that it has no effect on my future only makes studying it more fun.
anyone from purdue? i hate linear!
Khhhhaaannnnn!!!!
SCHMIDTTY!
go Purdue! also taking linear second midterm lol ... Love your videos Sal, very helpful in understanding these abstract concepts that always get muddled in my head by the book.
Thank you. Things in my linalg book become too complicated when they just throw theorems and lemmas at you without explaining what the formulas actually mean....
you r my new hero lol! thank you so much
Now I see how fortunate I am that I got that explained pretty well at school in the first place and I do not have to seek the titbits of inspiration online. But for those who do not have that privilege, Khan can truly be a real saviour.
great sir!! i love listening to your way of explaining things
I got really excited when I typed in the gram-schmidt process on google and saw that the khan academy has a video on it!
hey so i just took my final exam today and a question was "explain the gram schmidt process"....and i totally drew these diagrams and explained everything. Awesomeness.
thaaaanks a lot
Very nice and easy tutorial! I love it. But shouldn't there be brackets at: y3 = v3 - ( (v3*u1)*u1 + (v3*u2)*u2) ) Greetings and thank you very much!!!
Gram-Schmidt is the shit
Wonderful. The Gram-Schmidt Process was like a space science for me before I found this video. Thanks a lot.
i cant get it cuz at school we use a diiferent formula for projection. projF on a :[( F.a) / (a.a)]. a
You are a life saver!
You're fantastic!
On 5:00 you say V1 is not going to be on line spanned by U1. Actually it should be V2 and not V1 that is not going to be on line spanned by U1. Am i right? You are doing a great job. Keep it up :))
@redougulas I have second midterm tomorrow
well a in this case is normal (length of one) so a . a is just one
There is a small mistake at 16:09 the plus in the pasted part should become a minus.
You are the man! Saving my ass from my shitty professor!
me too :P
agreed. khan you are indeed the man.