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
@sitproperlywhilewatchingph4232 жыл бұрын
Thanks man This really helps I wish u a happy life 🙂
@jacobharris30023 жыл бұрын
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.
@theaveragepro17492 жыл бұрын
this is my current predicament, linear algebra 2 is rough
@anonymous9217w2 Жыл бұрын
@@theaveragepro1749 2 is actually way easier than 1, may be u r dumb af
@daylyght36545 жыл бұрын
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.
@ahmedbadday67412 жыл бұрын
Thanks professor Dave!
@cr316022 күн бұрын
Don't donate money to kuffar. He hates your religion.
@lucynowacki33272 жыл бұрын
Nice, but in 6:55 should be plus. Namely, to recover vector in the original basis.
@kirancp47582 жыл бұрын
yes
@braydenchan138 Жыл бұрын
I figure out for a while.
@adityapaul8508 Жыл бұрын
thanks for clearing that ... i was also a bit confused
@AkimboFennec3 жыл бұрын
Thanks
@bao58605 жыл бұрын
6:56 it is clearly U1 + 1/3 U2 , not (-)
@tauhidanwar35124 жыл бұрын
yes it should be U1 + 1/3U2
@trillonairesclub23294 жыл бұрын
no its - remember he got the determinant as - 1/3
@juergon694 жыл бұрын
@@trillonairesclub2329 wHY?
@anandailyasa25304 жыл бұрын
@@trillonairesclub2329 oke if it is -1/3 try subtitute u1 and u2 to the equation and see
@madhusudhanannarasimhan9875 Жыл бұрын
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.
@randymartin55002 жыл бұрын
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
@rasathashokumar80702 жыл бұрын
I think so
@annamoskalew54652 жыл бұрын
There is a mistake for sure. It should be +1/3.
@BraveGisgo Жыл бұрын
yeah i rewatched the video trying to see if i had missed something, but yeah
@rollychairs5 жыл бұрын
Just in time for my linear algebra exam
@unbendedurchin18215 ай бұрын
Was the degree worth it
@timothypulliam21774 жыл бұрын
I learned more in your video than years of academia. Cheers.
@BoZhaoengineering3 жыл бұрын
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!
@dawintch45964 жыл бұрын
8:16 Confirmed, Basis changes are all about UWU
@robin14185 жыл бұрын
You deserve at least 10x the number of subscribers.
@emilyisreading_2 жыл бұрын
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!
@davidgruen74233 жыл бұрын
7:57 As a mechanic this makes me pumped up!
@ignaciodelavega4631 Жыл бұрын
4:58 "We have to get rid of you". I knew I was useless, but I think saying that was unecesarry.
@sasugamegami5113 Жыл бұрын
4:58 that hit right in the feels
@piupolino2618 Жыл бұрын
7:01, U1 - 1/3 U2 would yield to the vector being 0,1? It would only work if it's + U2
@AndrewLyon233 жыл бұрын
This just confused me more.
@yuvikavarun3 ай бұрын
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 😭😭
@yogitajindal31495 ай бұрын
Great explanation Thank you so much 🙏🏻
@akashtiwari3432Ай бұрын
Thank you so much for this this type of explanation your teaching way is really appreciatable. mind-blowing
@socialkindle1314 Жыл бұрын
6:59 shouldn't it be + instead of -1/3u2
@kapilprajapat-qb6cz10 ай бұрын
6:55 there should be u1 + u2/3
@aku75989 ай бұрын
Graphically v=u1+(1/3)u2
@aliensoup24205 жыл бұрын
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.
@JimmyCerra3 жыл бұрын
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).
@hopewellmuzavazi2365 Жыл бұрын
Proffesor dave explains for sure
@rockyshepheard60542 жыл бұрын
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)
@mathadventuress3 жыл бұрын
for the comprehension written in terms of u1= and u2= how did it end up with (16/9)u1+(13/9)u2?
@zbziyagil3 жыл бұрын
I think there is a calculation mistake I have found 24/9u1+1/3u2
@sohamsantra75482 жыл бұрын
@@zbziyagil It's correct
@kheangheng47373 ай бұрын
@@sohamsantra7548 I don't think the solution is right
@emreeren842524 күн бұрын
it has to be (15/9)u1+(12/9)u2
@AriaHarmony2 жыл бұрын
I feel that doing row reduction using Gaussian elimination is easier, it also works on any matrix including rectangular matrices.
@dddhhj87092 жыл бұрын
🥸 tedious man row reduction
@nirmalkarthik58922 жыл бұрын
This video was awesome; it was so clear and thorough!
@MyHvorfor Жыл бұрын
4:55 "In order to isolate this v' term, we have to get rid of YOU" *leaves video in sad desperation*
@Imran52Feb2 жыл бұрын
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.
@Kevinfreddo2 жыл бұрын
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.
@abdisamad_5 жыл бұрын
Proff Dave🔥
@dddhhj87092 жыл бұрын
thank you so much .I learned it in such a short time Im suprised
@westonley92944 жыл бұрын
Very helpful video. Although , I think solving a system of equations is faster than using an inverse matrix for the standard basis.
@trustkibou Жыл бұрын
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.
@user-wr4yl7tx3w Жыл бұрын
really well explained
@maxpercer71192 жыл бұрын
why is it called transition matrix (if we use the inverse transition matrix in practice) ?
@just4simplegg4288 ай бұрын
Let's change things up ... xD I love this guy!
@_simply2say5 жыл бұрын
Cool explanation
@sohb1433 жыл бұрын
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).
@luagomesmartins30583 жыл бұрын
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!
@shurmurray5 жыл бұрын
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 =)
@emreeren842524 күн бұрын
it has to be (15/9)u1+(12/9)u2
@trevorkipkoech-ey1mk24 күн бұрын
yeeah for sure
@brd87644 жыл бұрын
There are three axis, three dimension and three basis. One is horizontal, other is vertical and third is perpendicular.
@businesstuber3978 Жыл бұрын
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.
@omerfarooq8223 Жыл бұрын
Great job man
@mohdaymanhussainmohdaymanh5574 Жыл бұрын
Best explanation
@vsmn190 Жыл бұрын
You're incredible.
@mlworks3 жыл бұрын
You're awesome Prof.
@noodle77882 ай бұрын
Thanks dave
@trillonairesclub23294 жыл бұрын
thank you God bless you
@sriyasomanatham2 жыл бұрын
can anyone explain the 2nd question in the exercise?
@yasmeennour472 жыл бұрын
+1
@tempname82635 жыл бұрын
Ugh. I had always thought change of basis is a simple operation and it's easy to teach that.
@maxpercer71192 жыл бұрын
the notation is quite convoluted BUT IT MAKES SENSE (sorry caps) - thx professor dave
@thepleasantcatprincess3 жыл бұрын
Thank you so much
@alexandrkorkin-p5rАй бұрын
Okay I’m following… I think I get it… 8:40 I do not get it
@hazza62653 жыл бұрын
isn't it v=u1+1/3*u2 not '-'?
@sekharp33052 жыл бұрын
Very clear
@omisingh96774 жыл бұрын
HANDS UP IF THE HAIRCUT IS BETTER THEN ORIGINAL
@adamsonthomas33308 ай бұрын
does this work for R3 and above?
@furkankamaci61805 ай бұрын
You are great
@brianbrian48994 жыл бұрын
How come no one points out he's wearing exact same T-shirt every single video??
@ProfessorDaveExplains4 жыл бұрын
Every series gets a shirt. Check out a different series, see a different shirt.
@asht77884 жыл бұрын
U da best
@iboa69383 жыл бұрын
what if the basis is a non square matrix
@monakolishi87719 күн бұрын
but(2,3)=(1,2)+(1/3)*(3,3),isn't it?
@jamesa.6464 жыл бұрын
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
@pistoletik7772 жыл бұрын
super! respect
@plusk3439 ай бұрын
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
@BoyaoZhang-me8cg Жыл бұрын
I LOVE U!!!!!!!!
@memevideos74616 күн бұрын
@xingzhang49852 жыл бұрын
you are my god!
@justinsankar11645 жыл бұрын
400k!
@anandailyasa25304 жыл бұрын
❤️❤️❤️❤️❤️
@unrealdevop2 жыл бұрын
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.