Tensors for Beginners 1: Forward and Backward Transformations (REMAKE)

I made a mistake in the original version of this video that has been confusing people for years. Super late, but trying to make amends.

[thedorantor]

The fact that after so many years you still bother to answer questions from comments under old videos and even remake a 4 year old video... You're an amazing teacher, nothing but respect for you!

[Jonas-Seiler]

I have never seen the visualisation of vectors you show at the very end of the video before. This is basically an epiphany for me. Taking the basis to be rows while taking the components to be columns suddenly makes everything I have heard about vectors and covectors make sense. This video has already been truly invaluable to me.

[atzuras]

This remake is very welcome. One of the best introductory courses I found on this plattform.

[linuxp]

I'd like to thank you for your care, even on such early lessons like that. Personally, your lectures helped me in a presentation about Schwarzschild's solution to Einstein's Field Equations

[dalisabe]

Excellent presentation. It assumes that the student know very little or nothing. This shows experience in teaching and good common sense on the part of the instructor.

[nstrisower]

WHAT THE FUCK HOW DID I NEVER MANAGE TO LEARN ABOUT THAT WAY OF MULTIPLYING MATRICES
that alone makes this video a literal godsend tbh thank u so much

[etiennecameron]

Thank you Chris. You answered the exact question I had yesterday in your tensor calculus series. Didn't understand why the jacobian matrix was not transposed. Basis vectors are covariant. Covariant vectors are covectors. Covectors multiply from the left. Thank you

[michaelzumpano]

I watched your series on general relativity. It was awesome! You make these subjects so navigable. I hope you never stop.

[phijiks]

I was reading quite a few books on Tensors for beginners, and then i came across your series of Tensors for beginners(many years ago when you just started making those initial Initially it felt the best source for learning tensors however after the error in this particular video and then the correction video you made earlier it all felt so much confusing that i tried many times on multiple occasions to clear things up and make a coherent sense of all the books i have and your (this particular) video but i couldn't.... Ultimately each time i had to drop this topic and move further only to get stuck in advance as I didn't know basics

I really hope this time when I'm going to give a new try with this video, i really can make a sense of all the books and your videos and finally understand the proper basics of it....


Meanwhile all these years i was just wondering you moved ahead continuing your series all the way up to General relativity and it made me wonder even if you could revisit your older videos and make a correction for people like me so I can reach the advance videos with you as In hopes i always had your notifications And woah ho finally you did that today I am so so much grateful for you, for that I'm a high school physics teacher, but Tensors has always been something i really really want to understand and learn properly....and you are the best source I have found till date, again thankyou for this correction video

[Mikey-mike]

Thanks, EigenChris.

Actually, your original video on this subject with your mistake was a good pedagogic device to point the matrix entries of the individual equations.

You are one of kind, an excellent teacher.

[jonpritzker]

Heaping on the deserved laudations. Your effort is noble and nearly brings me to tears. Thank you.
I've studied row and column multiplication, and I started Arfken's Math for physicists, where one of the opening problems is rotating a 2d basis, and I've heard people say "nevermind that torque is a pseudo bi-vector, " but I did not know linear algebra and that Arfken stuff was baby tensor math. Your presentation has got me excited, because it might not be as scary as I thought :D
Second smily for emphasis :D

[MrMilesfinn]

Thanks from an experimental physicist--great work.

[johnsimspon]

kudo man. That mistake has caused me much difficulty for years.

[robertlouis]

Wow I just found this video for the first time and haven't watched it yet but I'm sure glad whatever mistake was in the original one I missed because by the sounds of these comments it was a doozy.

[msontrent]

Excellent explanation. Thank you for taking the time ...

[manaayek]

Your defining linear algebra terms better than when i actually took linear algebra. Its all clicking now.

[mMaximus]

Hopefully you updated/continue this series!

[aditya_a]

Hey, thanks for this series! Just a question — In the very beginning, you say that the matrix representing the "forward transformation" eats vectors in the old, blue basis and outputs vectors in the new, red basis. But this doesn't quite sit right with me. If I feed the vector v with components (1, 0) into this matrix via F*v, the result is (2, 1). So clearly, what seems to be happening is F eats vectors in the red, what you call "new" basis, such as (1, 0), and outputs vectors in the blue, what you call "old" basis...

[jonnymahony]

to understand all of this you really have this notation and linear algebra manipulations under your belt, same if true for quantumfieldtheory, I'm often lost in notation 😂

[sdsa]

awesome! I get that they are inverses of each other… is seems like it would be easy to directly derive one from the other… just by reversing the left-right vertical and flipping the sign on the right-left vertical… but not sure how to prove that.