Tensors for Beginners 9: The Metric Tensor

Starting to lose steam again. I feel the way I'm editing videos is really inefficient.

I have 3 more videos planned for the non-calculus videos. After that I'll take a break and do some tensor calculus vids.

[cermet]

What an incredibly good and straight forward explanation of the Metric tensor! Using the Pythagorean theorem approach was brilliant and made so much sense! Seeing how it fails for non - orthonormal basis and then how the metric tensor correct both the basis and vector coefficients was very good. You have such an intuitive approach that makes total sense in the real world rather than the ratified math or physics approach (when applied blindly and then the student must just accept the concept rather then "see" it as in this vid.)

[srfnyu]

I've been trying to teach myself general relativity for a while and tensors have without a doubt been my Achiles heel. So glad I found these videos. You're doing a great job!

[ahmedabbas]

I've tried many videos and books on tensors but never come across such a clear explanation of the subject like this which in itself a sign that the teacher has mastered his stuff and understood the subject way better than those who cannot present it like him in this clear and lucid manner.

[ryanj]

On the off-chance that a watcher happens to be working through Munkre's excellent Analysis on Manifolds while watching: This video explains exactly what's going on under the hood in Exercise 4 of Section 1.1. (I dimly remembered this problem while watching this fantastic video!)

[brilinos]

Your videos are real pleasure to watch. Please continue as soon as possible. Looking forward to tensor calculus. Thanks for your work!

[stephaniebeiram]

There needed to be a mic drop at 14:38. This series is by far the best and most intuitive explanation of tensors I have ever seen. Thank you for this gift!

[buramjakajil]

I must say, you're videos are superb! You beat many professors I know! Referencing to other earlier comments here, I believe the ability to explain things relates very much to how well you actually understand what you're talking about. Quoting Einstein: "If you can't explain it simply, you don't understand it yourself well enough". But you clearly seem to know what you're talking about ;) You're doing an important work. Thank you very much and keep it up!

[przadka]

I just wanted to espress my gratitute for your work Chris! I have decided to learn tensors this year, as a gateway to better understand differential geometry. Your series and the work of @MathTheBeautiful are extremely valuable for me on that journey :)

[TarunKumar-qrfb]

Just started this playlist yesterday, completing today. I never stayed (or completed) on any playlist this long. I am in love with this series. Looking forward to start Tensor calculus tomorrow .

[rebollo]

U r genius bro! It looks very easy in the way you say it, I am already an Aerospace engineer, and i have never seen such a simple explanation. Very well done!

Best regards from Amsterdam!

[meenakshiiyer]

i request you to make a series on linear and abstract algebra too.
please please
you outclass every video that has been present in youtube so far.

[pellythirteen]

Wow. For the first time in my life I am really getting a grasp on what tensors are and how they work.
This is due to the excellent way it is presented. Very to the point, very clear graphics and a pleasant pace.
The author assumes the reader has at least a highschool level of maths.

[humphreyearwicker]

Really enjoyed these videos. Hope you produce more. The exposition is fantastically clear and concise!

[UniversoNarrado]

Man, you are a natural professor! Your videos are amazing and incredibly helpful. Thanks a lot for the job on tensor calculus. It's the best thing I have found on the entire internet (and man, I have searched about this).
Thanks. Regards from Brazil! (Where are u from?)

[tzaidi]

Awsome series! It is a service to humanity to make these available for free. Thanks.

[dennisbrown]

Amazing! This clarifies so much in a manner no one else ever does and connects so much that previously, I was confused or simply did not see the connections. The parallel examples really explains this in such an intuitive manner. You need to have a "Tip" button. Your time is deserving of compensation - I'd certainly pay for a book like this!

[vivalibertasergovivitelibe]

Thank you so much. My physics prof was just like "well this is a tensor and this is what it does in relativity" without any explanation as to what they truely are. You give such a great straight forward perspective on them. Just watching the few videos so far has given me so much more understanding on what we actually did in the lectures and helped me freshen up and get a new perspective linear algebra (my prof loved proofs but nearly never gave any visual intuition)
Thank you so much from a physics student who is thanks to you not afraid of tensors anymore ;)

[akshatpathrikar]

The greatest explanation of the metric tensor there is. Thanks, Chris.

[iputuwidiantara]

Thank you very much kind sir. It's amazing to see how that dot product in the end show phytagoras for the orthonormal case

[labalimbu]

Thanks a lot for making me understand what tensor is. You are such a underrated mathematician.