This is the simplest explanation of change of basis I have ever seen. I ended up taking two linear algebra courses in college. The first I went through was fine and I was able to apply change of basis easily enough to pass with an A. The second somehow made me more confused than before, probably do to different notation of things and I don't think my professor and textbook were as good. Now I feel like this video has finally cemented the concept and helped me figure out where the equations come from.
0:09 Why do we change basis? 0:18 0:25 Recalling previous knowledge of vectors 1:06 Vector Basis Change basis= New Axis, new coordinates 1:52 Writing Vectors with new coordinates in a new basis 2:09 The Same Vector, with different coordinates 3:02 Doing a little Algebra
I have to say this is the simplest interpretation of Change of basis. No fancy anime. Just write the simplest math notation and explain it in plain language. Just awesome! The simplest makes the easiest to understand!
At 6:55 , is the sign correct? Why is there a minus sign when the signs cancelled out during the multiplication of -1/3 . New basis should be V = U1 + 1/3U2
you're a lifesaver (literally) I was planning on dropping out of my uni cus of linear algebra, this was my last try, and I'm glad I took it, thank youu so much 😭😭
I am an undergrad chem major who is teaching myself graduate level molecular orbitals theory, and it’s still insane to me how literally all graduate chemistry is linear algebra.
I don't like this v prime notation, it seems that poeple, including myself, get confused. Instead it should be expressed as coefficients c1 and c2, which applied on new basis vectors u1 and u2. These coefficients specify how much of each new basis vector is needed to construct the vector v.
Here 1, 2 for u1 and vector u2 3, 3 are the I,j coordinates for new bases vectors u1 is a vector (1i 2j )and u2 is a vectorb( 3i 3j) in the i-j plane ? 0ur job here is scaling u1 and u2 so that they form the given vector.
two years late, but not necessarily; depending on the span, there could potentially be any number of dimensions; this math works for an n-dimensional system.
I saw that while a change of basis the origin remains the same, what should we do if the origin is also changed, for example, the origin in system 1 is (0,0), but in system 2 it is moved to the coordinates (2,1).
hi:) you probably dont need this answer anymore haha but im answering for anyone wondering the same. Linear algebra is about a special type of transformations, linear transformations. A transformation is not linear if the origin changes place! (For being linear the origin cant change place and straight lines must stay straight). Hope this helps!
Man, this vector math is insanely hard to grasp. I think it's mostly because all the videos explaining it do so in terms of arbitrary letters rather than real world scenarios....I can't find any decent videos on this in reference to manipulating things inside a 3-dimensional world like a game....for example if I had two actors in a game. One actor is facing another actor and moving towards it (Perhaps at an Angle) and the actor facing that other actors position shifted to the left....how would I determine how far it is now offset from that other actors position if it were still rotated in the same direction....stuff like this seems like it should be elementary stuff and yet I have scoured the internet and not once seen anything remotely close to this in any of the sources I have found.
This is the simplest explanation of change of basis I have ever seen. I ended up taking two linear algebra courses in college. The first I went through was fine and I was able to apply change of basis easily enough to pass with an A. The second somehow made me more confused than before, probably do to different notation of things and I don't think my professor and textbook were as good. Now I feel like this video has finally cemented the concept and helped me figure out where the equations come from.
this is my current predicament, linear algebra 2 is rough
@@theaveragepro1749 2 is actually way easier than 1, may be u r dumb af
You have no idea how much I do appreciate "this" video! I almost quit linear algebra until I find your video.
Thank you so much.
Thanks
0:09 Why do we change basis? 0:18
0:25 Recalling previous knowledge of vectors
1:06 Vector Basis
Change basis= New Axis, new coordinates
1:52 Writing Vectors with new coordinates in a new basis
2:09 The Same Vector, with different coordinates
3:02 Doing a little Algebra
Thanks man
This really helps
I wish u a happy life 🙂
Thanks professor Dave!
Don't donate money to kuffar. He hates your religion.
That was one of the simplest videos on this topic that I came across. I am glad I did. You make it easy. Thank you.
I have to say this is the simplest interpretation of Change of basis. No fancy anime. Just write the simplest math notation and explain it in plain language. Just awesome! The simplest makes the easiest to understand!
I learned more in your video than years of academia. Cheers.
Thank you so much. I was really confused on change of basis but after watching this I feel way more confident for my linalg final!
Nice, but in 6:55 should be plus. Namely, to recover vector in the original basis.
yes
I figure out for a while.
thanks for clearing that ... i was also a bit confused
At 6:55 , is the sign correct? Why is there a minus sign when the signs cancelled out during the multiplication of -1/3 . New basis should be V = U1 + 1/3U2
I think so
There is a mistake for sure. It should be +1/3.
yeah i rewatched the video trying to see if i had missed something, but yeah
Just in time for my linear algebra exam
Was the degree worth it
You deserve at least 10x the number of subscribers.
6:56 it is clearly U1 + 1/3 U2 , not (-)
yes it should be U1 + 1/3U2
no its - remember he got the determinant as - 1/3
@@trillonairesclub2329 wHY?
@@trillonairesclub2329 oke if it is -1/3 try subtitute u1 and u2 to the equation and see
you're a lifesaver (literally) I was planning on dropping out of my uni cus of linear algebra, this was my last try, and I'm glad I took it, thank youu so much 😭😭
8:16 Confirmed, Basis changes are all about UWU
7:57 As a mechanic this makes me pumped up!
I am an undergrad chem major who is teaching myself graduate level molecular orbitals theory, and it’s still insane to me how literally all graduate chemistry is linear algebra.
6:55
there should be u1 + u2/3
Graphically v=u1+(1/3)u2
Great explanation Thank you so much 🙏🏻
4:55 "In order to isolate this v' term, we have to get rid of YOU"
*leaves video in sad desperation*
4:58 that hit right in the feels
Thank you so much for this this type of explanation your teaching way is really appreciatable. mind-blowing
I don't like this v prime notation, it seems that poeple, including myself, get confused. Instead it should be expressed as coefficients c1 and c2, which applied on new basis vectors u1 and u2. These coefficients specify how much of each new basis vector is needed to construct the vector v.
7:01, U1 - 1/3 U2 would yield to the vector being 0,1? It would only work if it's + U2
Proffesor dave explains for sure
This video was awesome; it was so clear and thorough!
Very helpful video. Although , I think solving a system of equations is faster than using an inverse matrix for the standard basis.
You're right... he said it was simpler, but I think he meant to say that it's useful to see that action be made for future topics in LA.
I feel that doing row reduction using Gaussian elimination is easier, it also works on any matrix including rectangular matrices.
🥸 tedious man row reduction
for the comprehension written in terms of u1= and u2= how did it end up with (16/9)u1+(13/9)u2?
I think there is a calculation mistake I have found 24/9u1+1/3u2
@@zbziyagil It's correct
@@sohamsantra7548 I don't think the solution is right
it has to be (15/9)u1+(12/9)u2
4:58 "We have to get rid of you". I knew I was useless, but I think saying that was unecesarry.
I keep getting screwed up - when I'm given a system of vectors, I never know if I'm supposed to use the vectors as rows or columns in the matrix.
each vector goes in the column. So the first row are all the x values, second row are the y values, etc... (and so on for higher dimensional vectors).
Here 1, 2 for u1 and vector u2 3, 3 are the I,j coordinates for new bases vectors u1 is a vector (1i 2j )and u2 is a vectorb( 3i 3j) in the i-j plane ? 0ur job here is scaling u1 and u2 so that they form the given vector.
6:59 shouldn't it be + instead of -1/3u2
There are three axis, three dimension and three basis. One is horizontal, other is vertical and third is perpendicular.
two years late, but not necessarily; depending on the span, there could potentially be any number of dimensions; this math works for an n-dimensional system.
really well explained
Thanks dave
Best explanation
thank you so much .I learned it in such a short time Im suprised
Cool explanation
Great job man
You're incredible.
You're awesome Prof.
thank you God bless you
Would it be less confusing to write the new u basis eq just like the std ij one? ie.
V(arrow) = v sub 1 times m (hat) + v sub 2 times n ) hat)
The final v in the new basis should be u1 + 1/3 u2 not negative as in video
thanks i was getting so confused bcuz i solved it as a system rather than invert U and i got 1 and 1/3.
Thank you so much
Let's change things up ... xD
I love this guy!
why is it called transition matrix (if we use the inverse transition matrix in practice) ?
This just confused me more.
Dont bother with this video when we have 3blue1brown
Its because you didnt have the BASIS information before watching this video.
I saw that while a change of basis the origin remains the same, what should we do if the origin is also changed, for example, the origin in system 1 is (0,0), but in system 2 it is moved to the coordinates (2,1).
hi:) you probably dont need this answer anymore haha but im answering for anyone wondering the same. Linear algebra is about a special type of transformations, linear transformations. A transformation is not linear if the origin changes place! (For being linear the origin cant change place and straight lines must stay straight). Hope this helps!
4:30 made no sense to me. how did you get v to be [2 3]
Very clear
can anyone explain the 2nd question in the exercise?
+1
I remember me sitting on my very first lection of linear algebra. 5 minutes later I know how to make a 3D-graphics and was eager to get to my PC =)
You are great
isn't it v=u1+1/3*u2 not '-'?
Ugh. I had always thought change of basis is a simple operation and it's easy to teach that.
the notation is quite convoluted BUT IT MAKES SENSE (sorry caps) - thx professor dave
does this work for R3 and above?
Okay I’m following… I think I get it…
8:40 I do not get it
U da best
what if the basis is a non square matrix
super! respect
but(2,3)=(1,2)+(1/3)*(3,3),isn't it?
HANDS UP IF THE HAIRCUT IS BETTER THEN ORIGINAL
Thanks for this after watchin' this video I was able to finish my shit
Edit: I mean my literal shit, not my homework. I havent started that yet
bruh dont use v to represent constant because in most books it is used to represent vectors and it can be confusing for beginners to relise
I LOVE U!!!!!!!!
How come no one points out he's wearing exact same T-shirt every single video??
Every series gets a shirt. Check out a different series, see a different shirt.
it has to be (15/9)u1+(12/9)u2
yeeah for sure
you are my god！
400k!
❤️❤️❤️❤️❤️
Can't finish the video, too many adds makes it too long to watch.
Man, this vector math is insanely hard to grasp. I think it's mostly because all the videos explaining it do so in terms of arbitrary letters rather than real world scenarios....I can't find any decent videos on this in reference to manipulating things inside a 3-dimensional world like a game....for example if I had two actors in a game. One actor is facing another actor and moving towards it (Perhaps at an Angle) and the actor facing that other actors position shifted to the left....how would I determine how far it is now offset from that other actors position if it were still rotated in the same direction....stuff like this seems like it should be elementary stuff and yet I have scoured the internet and not once seen anything remotely close to this in any of the sources I have found.
i dont understand.bay
Too complicated !!!!
thanks