Change of Basis

  Рет қаралды 267,495

Professor Dave Explains

Professor Dave Explains

Күн бұрын

Пікірлер: 105
@michaelpisciarino5348
@michaelpisciarino5348 5 жыл бұрын
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
@sitproperlywhilewatchingph423
@sitproperlywhilewatchingph423 2 жыл бұрын
Thanks man This really helps I wish u a happy life 🙂
@jacobharris3002
@jacobharris3002 3 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.
@theaveragepro1749
@theaveragepro1749 2 жыл бұрын
this is my current predicament, linear algebra 2 is rough
@anonymous9217w2
@anonymous9217w2 Жыл бұрын
@@theaveragepro1749 2 is actually way easier than 1, may be u r dumb af
@daylyght3654
@daylyght3654 5 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.
@ahmedbadday6741
@ahmedbadday6741 2 жыл бұрын
Thanks professor Dave!
@cr3160
@cr3160 22 күн бұрын
Don't donate money to kuffar. He hates your religion.
@lucynowacki3327
@lucynowacki3327 2 жыл бұрын
Nice, but in 6:55 should be plus. Namely, to recover vector in the original basis.
@kirancp4758
@kirancp4758 2 жыл бұрын
yes
@braydenchan138
@braydenchan138 Жыл бұрын
I figure out for a while.
@adityapaul8508
@adityapaul8508 Жыл бұрын
thanks for clearing that ... i was also a bit confused
@AkimboFennec
@AkimboFennec 3 жыл бұрын
Thanks
@bao5860
@bao5860 5 жыл бұрын
6:56 it is clearly U1 + 1/3 U2 , not (-)
@tauhidanwar3512
@tauhidanwar3512 4 жыл бұрын
yes it should be U1 + 1/3U2
@trillonairesclub2329
@trillonairesclub2329 4 жыл бұрын
no its - remember he got the determinant as - 1/3
@juergon69
@juergon69 4 жыл бұрын
@@trillonairesclub2329 wHY?
@anandailyasa2530
@anandailyasa2530 4 жыл бұрын
@@trillonairesclub2329 oke if it is -1/3 try subtitute u1 and u2 to the equation and see
@madhusudhanannarasimhan9875
@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.
@randymartin5500
@randymartin5500 2 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
@rasathashokumar8070
@rasathashokumar8070 2 жыл бұрын
I think so
@annamoskalew5465
@annamoskalew5465 2 жыл бұрын
There is a mistake for sure. It should be +1/3.
@BraveGisgo
@BraveGisgo Жыл бұрын
yeah i rewatched the video trying to see if i had missed something, but yeah
@rollychairs
@rollychairs 5 жыл бұрын
Just in time for my linear algebra exam
@unbendedurchin1821
@unbendedurchin1821 5 ай бұрын
Was the degree worth it
@timothypulliam2177
@timothypulliam2177 4 жыл бұрын
I learned more in your video than years of academia. Cheers.
@BoZhaoengineering
@BoZhaoengineering 3 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!
@dawintch4596
@dawintch4596 4 жыл бұрын
8:16 Confirmed, Basis changes are all about UWU
@robin1418
@robin1418 5 жыл бұрын
You deserve at least 10x the number of subscribers.
@emilyisreading_
@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!
@davidgruen7423
@davidgruen7423 3 жыл бұрын
7:57 As a mechanic this makes me pumped up!
@ignaciodelavega4631
@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
@sasugamegami5113 Жыл бұрын
4:58 that hit right in the feels
@piupolino2618
@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
@AndrewLyon23
@AndrewLyon23 3 жыл бұрын
This just confused me more.
@yuvikavarun
@yuvikavarun 3 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 😭😭
@yogitajindal3149
@yogitajindal3149 5 ай бұрын
Great explanation Thank you so much 🙏🏻
@akashtiwari3432
@akashtiwari3432 Ай бұрын
Thank you so much for this this type of explanation your teaching way is really appreciatable. mind-blowing
@socialkindle1314
@socialkindle1314 Жыл бұрын
6:59 shouldn't it be + instead of -1/3u2
@kapilprajapat-qb6cz
@kapilprajapat-qb6cz 10 ай бұрын
6:55 there should be u1 + u2/3
@aku7598
@aku7598 9 ай бұрын
Graphically v=u1+(1/3)u2
@aliensoup2420
@aliensoup2420 5 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.
@JimmyCerra
@JimmyCerra 3 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
@hopewellmuzavazi2365 Жыл бұрын
Proffesor dave explains for sure
@rockyshepheard6054
@rockyshepheard6054 2 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)
@mathadventuress
@mathadventuress 3 жыл бұрын
for the comprehension written in terms of u1= and u2= how did it end up with (16/9)u1+(13/9)u2?
@zbziyagil
@zbziyagil 3 жыл бұрын
I think there is a calculation mistake I have found 24/9u1+1/3u2
@sohamsantra7548
@sohamsantra7548 2 жыл бұрын
@@zbziyagil It's correct
@kheangheng4737
@kheangheng4737 3 ай бұрын
@@sohamsantra7548 I don't think the solution is right
@emreeren8425
@emreeren8425 24 күн бұрын
it has to be (15/9)u1+(12/9)u2
@AriaHarmony
@AriaHarmony 2 жыл бұрын
I feel that doing row reduction using Gaussian elimination is easier, it also works on any matrix including rectangular matrices.
@dddhhj8709
@dddhhj8709 2 жыл бұрын
🥸 tedious man row reduction
@nirmalkarthik5892
@nirmalkarthik5892 2 жыл бұрын
This video was awesome; it was so clear and thorough!
@MyHvorfor
@MyHvorfor Жыл бұрын
4:55 "In order to isolate this v' term, we have to get rid of YOU" *leaves video in sad desperation*
@Imran52Feb
@Imran52Feb 2 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.
@Kevinfreddo
@Kevinfreddo 2 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_
@abdisamad_ 5 жыл бұрын
Proff Dave🔥
@dddhhj8709
@dddhhj8709 2 жыл бұрын
thank you so much .I learned it in such a short time Im suprised
@westonley9294
@westonley9294 4 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
@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
@user-wr4yl7tx3w Жыл бұрын
really well explained
@maxpercer7119
@maxpercer7119 2 жыл бұрын
why is it called transition matrix (if we use the inverse transition matrix in practice) ?
@just4simplegg428
@just4simplegg428 8 ай бұрын
Let's change things up ... xD I love this guy!
@_simply2say
@_simply2say 5 жыл бұрын
Cool explanation
@sohb143
@sohb143 3 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).
@luagomesmartins3058
@luagomesmartins3058 3 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!
@shurmurray
@shurmurray 5 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 =)
@emreeren8425
@emreeren8425 24 күн бұрын
it has to be (15/9)u1+(12/9)u2
@trevorkipkoech-ey1mk
@trevorkipkoech-ey1mk 24 күн бұрын
yeeah for sure
@brd8764
@brd8764 4 жыл бұрын
There are three axis, three dimension and three basis. One is horizontal, other is vertical and third is perpendicular.
@businesstuber3978
@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
@omerfarooq8223 Жыл бұрын
Great job man
@mohdaymanhussainmohdaymanh5574
@mohdaymanhussainmohdaymanh5574 Жыл бұрын
Best explanation
@vsmn190
@vsmn190 Жыл бұрын
You're incredible.
@mlworks
@mlworks 3 жыл бұрын
You're awesome Prof.
@noodle7788
@noodle7788 2 ай бұрын
Thanks dave
@trillonairesclub2329
@trillonairesclub2329 4 жыл бұрын
thank you God bless you
@sriyasomanatham
@sriyasomanatham 2 жыл бұрын
can anyone explain the 2nd question in the exercise?
@yasmeennour47
@yasmeennour47 2 жыл бұрын
+1
@tempname8263
@tempname8263 5 жыл бұрын
Ugh. I had always thought change of basis is a simple operation and it's easy to teach that.
@maxpercer7119
@maxpercer7119 2 жыл бұрын
the notation is quite convoluted BUT IT MAKES SENSE (sorry caps) - thx professor dave
@thepleasantcatprincess
@thepleasantcatprincess 3 жыл бұрын
Thank you so much
@alexandrkorkin-p5r
@alexandrkorkin-p5r Ай бұрын
Okay I’m following… I think I get it… 8:40 I do not get it
@hazza6265
@hazza6265 3 жыл бұрын
isn't it v=u1+1/3*u2 not '-'?
@sekharp3305
@sekharp3305 2 жыл бұрын
Very clear
@omisingh9677
@omisingh9677 4 жыл бұрын
HANDS UP IF THE HAIRCUT IS BETTER THEN ORIGINAL
@adamsonthomas3330
@adamsonthomas3330 8 ай бұрын
does this work for R3 and above?
@furkankamaci6180
@furkankamaci6180 5 ай бұрын
You are great
@brianbrian4899
@brianbrian4899 4 жыл бұрын
How come no one points out he's wearing exact same T-shirt every single video??
@ProfessorDaveExplains
@ProfessorDaveExplains 4 жыл бұрын
Every series gets a shirt. Check out a different series, see a different shirt.
@asht7788
@asht7788 4 жыл бұрын
U da best
@iboa6938
@iboa6938 3 жыл бұрын
what if the basis is a non square matrix
@monakolishi8771
@monakolishi8771 9 күн бұрын
but(2,3)=(1,2)+(1/3)*(3,3),isn't it?
@jamesa.646
@jamesa.646 4 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
@pistoletik777
@pistoletik777 2 жыл бұрын
super! respect
@plusk343
@plusk343 9 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
@BoyaoZhang-me8cg Жыл бұрын
I LOVE U!!!!!!!!
@memevideos7461
@memevideos7461 6 күн бұрын
@xingzhang4985
@xingzhang4985 2 жыл бұрын
you are my god!
@justinsankar1164
@justinsankar1164 5 жыл бұрын
400k!
@anandailyasa2530
@anandailyasa2530 4 жыл бұрын
❤️❤️❤️❤️❤️
@unrealdevop
@unrealdevop 2 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.
@irem3450
@irem3450 8 ай бұрын
i dont understand.bay
@reamabdulsalam524
@reamabdulsalam524 Жыл бұрын
Too complicated !!!!
@OOFtheSecond
@OOFtheSecond 7 ай бұрын
thanks
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