Transpose Definition
ฝัง
- เผยแพร่เมื่อ 13 ก.ย. 2024
- Definition of the transpose
Have you ever wondered where the transpose comes from? In this video, I show that the transpose arises naturally in the setting of dual spaces. This should also illustrate why dual spaces are so important. Enjoy!
Transpose Example (Sequel): • Transpose Example
Check out my Dual Spaces Playlist: • Dual Spaces
Subscribe to my channel: / drpeyam
“Now what the hell does that have to do with matrices?”
You took the words right out of my mouth.
"Press F to say Field" LOL
I like to think about the transpose as turning all of our rows into columns and columns into rows.
I'm studying to enter a masters in applied math and your light-hearted videos in topology, analysis and linear algebra are helping me a lot! Sometimes I get overwhelmed with the tons of information and whatching you teaching these subjects with a smile in your face just keeps me on track. Thank you Dr. Peyam!
Awwww thanks so much!!!
9:45 bless you!
9:35 Bless you, Dr Peyam!
Thanks :)
Dr Peyam I adore your videos so much. Everytime I look at a new one, I want to learn more math, it is really beautiful thank you!
Dr Peyam, regarding the comment on this video about hyper planes - extremely briefly, and I say this as someone who hasn’t finished your dual space playlist, but who is very grateful that it exists!! (Never delete your videos) I wonder how hyper planes to a vector have anything to do with abstract functionals? A sketch of the link would be greatly appreciated. Love your work, channels like these have taught me all the maths I know pretty much
Hi Dr. Peyam,
could you make some videos about tensor products and the vector space ofalternating multilinearforms (generalized determinants)?
Lovely videos!
Thank you! And I don’t know much about those, sadly
@@drpeyam LOOK UP TED SHIFRIN 3510 HE'S A BEAST
@@drpeyam Hi Dr. Peyam, thank you very much for your kind answer. I'm not studying in America and in our curriculum "analysis on manifolds" bases on differential forms (which bases on tensors and alternating multilinear forms). "Analysis on manifolds" is taught in the module "Analysis 3" which contains Measure, Integration Theory and vector calculus.
Since you you will teach Vector Calculus in the winter I would be interested to know what your Vec. Calc. course will contain :)
Greets!
Thank you very much , I really appreciate what you do !!! Thank you!!!
THANKYOU SO MUCH SIR EVERYTHING JUST SEEMS SO CRYSTAL NOW
Transposes and dual spaces are used all the time in the real world, so any intuition helps. Given a vector (x0, x1, x2, x3), what is an equation for the hyperplane it is perpendicular to? What is the relationship between the scalar x^Tx and the rank-1 matrix xx^T? Understanding these things pays dividends.
Dr. Peyam, you are my hero. thank you so much for your wisdom
You’re welcome
Keep the great work, please! I think what u taught is 2nd course in Linear Algebra, which is very proof-based with little intuition in many Universities' math department. So, these video is really unique and helped me a lot in terms understanding the proof based math.
Thank you! And yes, it indeed is based on the second course in LA that I taught last spring, glad you’re enjoying it :)
9:36 Bless you!
i love these videos a lot thank you
You’re welcome!!!
Damn, that was a nice and relatively rigorous proof, you sold me on your content, will watch it all
Magic indices. Thank you very much.
Thank you!
Sorry for spamming, but I just wanted to say that I a) really liked that; b) will have to watch again (at least once) because I i) really liked that; ii) am really not up to speed with some of that, but I'm getting there.
Thanks for the great videos! Keep them coming (please).
Heyy! Thanks for the video! I'd like to know if is there any book which you recommend for matrix and linear algebra, because all i know don't show this amazing perspective?!
Definitely Friedberg Insel Spence, and Lay (the latter is more elementary)
e = 3 = pi
Also, I sent my afghan friend this clip where you talk about "youye/chickenbreast in farsi" and I wondered, where do you originally come from?
Maybe you could even make a video about yourself one day? Like, where you come from and what got you started with maths and all :)
Dr Peyam, I am a little confused for the T^T(gj)(vi) = gj(T(vi) at from 14:33. Here we want to prove T^T(g)(x) = g(T(x)). Is that a little kind of "circular reasoning"?
Why can't i give this video a like
Great series!
Also, you say that we want to show that the transpose matrix is also a transpose in the dual space definition, but the way you phrased made me wonder if there exist other ways to find a “transpose” of some matrix that isn’t actually its transpose matrix!
15:55 Why did you multiply ∑(from k =1 to m) A_ki with w_k?
Is the matrix of a linear transformation a "row of columns" or a "column of rows"?
Row of columns :)
@@drpeyam im assuming that plays into matrix representation when computing A=[T]betti of gamma since your T(vi) are columns of the matrix A for vi being an element of the basis for V.
That was awesome!
How do you correctly transform a normal vector to a plane as it a row vector which is a member of the dual space
If the field is over the complex numbers, does that mean we must replace 'T' with 'transpose conjugate'?
Yes
well done
Wait so the transpose operator is just the higher order flip function?
Yeah
wtf is a flip function? Never heard of that
beautiful! :)
can you transpose a function though?
So is this T transpose map the pullback of T?
Something like that
1:07 F
19:13
Press F to say Field
0:20 Eek! (pedant alert). You mean "raises the question". To "beg the question" is to assume the answer in your argument. For example, if you say "god exists because it says so in the bible", then you are "begging the question" because the only reason to think the bible is true is because god said so, which presupposes the existence of god.
Of course, "beg the question" is so often used in the sense of "raise the question" that I have really just wasted my time typing this: that's what it means now. And, while it might be a shame to lose this nice distinction, it's probably only debaters and logicians who'll really get upset, so: why worry?
Anyway, I should really put my OCD to bed and get on with watching the rest of the video. Because I'm here for the maths and not to nit-pick about out-dated definitions of once-obscure phrases.
Thanks so much! I finally got a good explanation for this!!!!
@@drpeyam Thanks! (I think you flatter me). I did finish the video and some of it is beyond me, so I shall watch it again until it isn't. I see all the steps, but sometimes the overall picture fuzzes out. That's what I love about maths: keep focusing in, and everything eventually becomes sharp. (Terrible analogy, sorry).