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.
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!!
1:28 How to ensure a basis is orthonormal. 5:55 Replace v2 with the orthogonal projection of v2 onto v1 and the vector component of u orthogonal to v1.
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.
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
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.
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.
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| ?
Vrig I thought the same thing when I was doing this in my Linear Algebra class 6 years ago. not sure why you're taking the dot product of the unit vector...the thing is, you still have to multiply by u_1 to get the projection because the dot product is just a number, not a vector
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....
Correct me if i am wrong but you are missing something. When u were making projections u forgot that for example V2 onto V1 is equal to (V2 dot U1)*u1 OVER lenght of u1. Why? Because projection of some vector lets say A onto some line s is equal to ||A||cos(angle between A and s) Furthermore if say that A vector is V2 then V2 dot u1= ||u1|| projection V2 onto V1 . So projection V2 onto V1 =V2 dot u1 OVER ||u1|| so u are missing to devide everytime with lenght of base vector
I don't understand quite why he claims that the projection of v2 on to the subspace v1 can be described as (v2.u1)u1. Can someone help me understand, or is there perhaps part of another video that I missed?
taking the dot product of 2 vectors gives you the product of how much the 2 vectors travel in 1 direction....but since u1 is a unit vector...so you can say the dot product 'v2.u1' gives you the component of v1 travelling in the direction of u1 ....though the dot product is just a number.....to actually specify that it is in the of direction 'u1' you multiply the dot product (v2.u1) by the vector u1 to give it direction..
V_3 is all the linear combinations of v_1, v_2 and v_3, which contains all the vectors in 3 dimension space(assuming it is R^3). in which space does the fourth basis vector v_4 live? Mathematically it's there, but where is it geometrically?
Aweri Blakely I’m a little late to answer but the denominator is missing because he’s using the unit vector, I had the same question at first. U = v1 / |v1|
For me, 20 minutes of this is worth more than a 2 hour lecture. Thank you!
Khan Academy coming in clutch right before my Linear Algebra final #KhanAcademyIsBetterThanNYU
Asia Suarez??
Interesting name. My name is Europe Patel
You were meant for each other. You need to have a child together and name it Antartica Koulibaly!!!
and thier grand kids must be barcelona and madrid
@@metra-2020 nah turkey would be better
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.
Read your book too. Sometimes videos aren’t necessary to fill the gaps the instructor doesn’t.
damn your U :p
Tutorials are really nice, and that's really helping. Thank you :)
This felt so intuitive... my mind is blown. Thank you for showing us why math is so cool!
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!!
A day before my optional resit of quantum mechanics and here Khan Academy is, saving the day again.
+Árón de Siún Here for my test of Mathematical Methods of Physics :p
Saving mathematic lives out here, thanks fam
1:28 How to ensure a basis is orthonormal.
5:55 Replace v2 with the orthogonal projection of v2 onto v1 and the vector component of u orthogonal to v1.
Man this guy's the best. Been using these vids since middle school, and I'm in grad school now. Thanks Khan Academy
I don't have words to show how grateful I feel now
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.
Thank you so much, i am so grateful to you Sal. You literally changed everything....
thank you khan academy ,it was really useful .i was struggling to understand hilbert space now you made it easy.
This is so well explained. I had to go back watch it twice though. But makes complete sense now. Thank you so much!!!!
Thanks kahn. You're really helpin me out with my math classes
great sir!! i love listening to your way of explaining things
It became clear later on in the video. thank you so much for making it free!
That awkward moment when you understand something in maths :') Thanksss!!
You're truly great at teaching! Thanks and good luck!
minor correction @2:15 he should've written " || u_1 || " instead of just " u_1 "
Explained so well! Thank you
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
无可想象的伟大作品，足以名垂青史的杰作！！！！！
I can't believe it, I'm starting to love Linear Algebra
Thank u so much ! This video really helps me a lots !
by the student from Tw
I am so confused.
join the club
these vids are great in conjunction with PAULS online math NOTES
Is there a video from khan that is about "inner product spaces"? Help would be greatly appreciated. Thanks!
This explanation blew my mind
Khan Academy saving students' asses all over again
why can't Professors teach like that in universities?
Minus that business right there.......love it.....
God bless you Khan! Thank you for your work! 😇
Perfect lecture. Thank you.
You are a life saver!
There is a small mistake at 16:09 the plus in the pasted part should become a minus.
Best Explanation EVER!
thx u so much😊😊😊😊😊
you r my new hero lol! thank you so much
omg 10 years ago!! how is life goin now?
Superb explanation!
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.
Yes, the sign changes, or you need to use parenthesis.
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.
Good evening
Could someone please explain to me why from proj(v1)v2 we have the result (v2*u1)*u1?
I didn't get it
Thanks in advice
Doing god's work!
Please give my exam for me :(
Thanks for the tutorial, great explanation :)
whosss the mann??? khansss the mannn
Do the orthnormal vector basis that we get by Gram-Schmidt are unique
No. Orthonormal bases are not unique.
Much appreciated!
thanks! i understood
Oh thank you so much !
hey what program are you using for recording/writing up that stuff?
love you Khan
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| ?
Vrig I thought the same thing when I was doing this in my Linear Algebra class 6 years ago. not sure why you're taking the dot product of the unit vector...the thing is, you still have to multiply by u_1 to get the projection because the dot product is just a number, not a vector
How do you know everything?
nice job ,easy to understand.
thaaaanks a lot
I...understand!
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....
thank you.
Sal got color blindness, at 14:25 he meant yellow vector not green
I'm quite curious, are the subtitles automatically generated? If not, what's going on at 1:46? lul
He said, "you can argue the zero vector is in there."
thanks
Correct me if i am wrong but you are missing something. When u were making projections u forgot that for example V2 onto V1 is equal to (V2 dot U1)*u1 OVER lenght of u1.
Why? Because projection of some vector lets say A onto some line s is equal to ||A||cos(angle between A and s)
Furthermore if say that A vector is V2 then V2 dot u1= ||u1|| projection V2 onto V1 .
So projection V2 onto V1 =V2 dot u1 OVER ||u1|| so u are missing to devide everytime with lenght of base vector
lowzyyy the sizes of u1 U2 etc are all 1 since it is orthaNORMAL. so you can divide by the size, but since it is 2, it doesn't change the outcome
yes, u1 is 1 and lenght is 1.
u is unit length so you divide by 1. check your calculations and think about it some more
I don't understand quite why he claims that the projection of v2 on to the subspace v1 can be described as (v2.u1)u1. Can someone help me understand, or is there perhaps part of another video that I missed?
taking the dot product of 2 vectors gives you the product of how much the 2 vectors travel in 1 direction....but since u1 is a unit vector...so you can say the dot product 'v2.u1' gives you the component of v1 travelling in the direction of u1 ....though the dot product is just a number.....to actually specify that it is in the of direction 'u1' you multiply the dot product (v2.u1)
by the vector u1 to give it direction..
Where can i find the bibliography you used for this lecture? Now I've got the idea but i'd like to read it ;/
V_3 is all the linear combinations of v_1, v_2 and v_3, which contains all the vectors in 3 dimension space(assuming it is R^3). in which space does the fourth basis vector v_4 live? Mathematically it's there, but where is it geometrically?
no where. We as humans do not have a spatial 4 th dimension.
After R^3 we do not consider geometry, only structures.
well a in this case is normal (length of one) so a . a is just one
I really wonder why not all profs and books explain that the same way
Why are the concepts of math always made so hard? Why they can't be shown in simple terms like in this video? Who benefits?
Some instructors are simpler than this video too
@redougulas
I have second midterm tomorrow
Proud to be a Bangladeshi!!.........
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!"
very hard...
❤❤❤❤
1.75 speed, thank ye, thank ye
i cant get it cuz at school we use a diiferent formula for projection.
projF on a :[( F.a) / (a.a)]. a
when you compute the projection, you missed the denominator no?
Aweri Blakely I’m a little late to answer but the denominator is missing because he’s using the unit vector, I had the same question at first. U = v1 / |v1|
@TheNef77
same story
SCHMIDTTY!
Gram-Schmidt is the shit
not all heroes wear capes.
"Its that easy"...lol
i love you
me too :P
IS there no audio?
1 professor disliked this video as it made him look bad.
he thought for the future 11years ago
You are the man! Saving my ass from my shitty professor!
@sherajr me too lol
@sherajr You must be in my class. I hate that lady.
You're just spitting English man 😅
I started clapping. :')
im cooked bruh
anyone from purdue? i hate linear!
Haha you repeat things a lot, like individual words :)
9 years ago :o, how is life treating you now?
@dragonzito mojado It all went downhill
You are my life saver!!
Thank you!!!
thank you!
Thanks man