Tensors for Beginners 10: Bilinear Forms

Looking forward to getting to the tensor product.
Really not looking forward to editing the videos...

[jackrubin]

I am 64 years old and a retired pharmacist with prostate cancer. Your videos explain something I’ve always wanted to know.

[JgM-iejy]

You consistently demonstrate the art of teaching as opposed to its lower form of merely telling. I studied engineering way before the internet became a public commodity and I can testify that the impact of a bad teacher extends far beyond his 45-hour course.

Changing course to include additional material even after completing 9 videos (which obviously took considerable time to put together) because you felt the need to complete the picture is another demonstration that you sincerely care about teaching.

And you even add value to your videos by promptly answering the questions that were raised. I make it a point to see what is in the comments section before starting the video just to make sure I do not miss anything. This is as close as it can get to actually attending a course delivered by a live professor who answers questions as they arise.

Your dedication in producing this series of videos is definitely a wonderful gift to people you do not even know.

[thankall]

I am a teacher for years using lots of slides in my lectures but still learned a lot from your teaching. Thanks.

[carlosorea]

I never comment on videos but I love your style of doing videos, I have never seen someone explaining like this in all the tutorials I have seen.
Fast and clear. Great job.

[ahmedsaadsabit]

I never comment, but all I want to tell you is Thanks, really, a gratitude you worked so hard on those PowerPoints one after one, for free and accessible for all of us. Thanks. The greatest point is I did understand so many things so clearly.
And best of Luck for the General Relativity, we are eagerly waiting!

[akarshchaturvedi]

Your no bs approach and great visualizations make your explanations better than most of them other videos out there.

[nickthepostpunk]

I have watched all your videos up to this point and I am really impressed with the wealth of motivation and intuition you provide. You have a real gift for this!

[augustuscaeserb]

you are a real teacher...with an itch...that makes you great from mere good

[johnstephens]

Excellent explanations. Very good visualizations, everything smooth and clean, on pace and straight to the point! Great video.

[jackrubin]

Thank you for your dedication and love of your subject.

[xjregvg]

Thank you very much, Chris! You are doing great job for us!

[limark]

This series of video is the best I have ever watched for mathematics ! I am a physics friend but not very good at mathematics. I want to learn tensor because to learn more about general relativity requires some tensor knowledge. I like this series of videos because it explains very clearly even though I may not be able to follow all the mathematical deduction processes !

[cobrajoshi]

Great would never know what great help u have been for me

[nikolaradakovic]

Chris I don't know what's your major, but you teach math better than 99% of high profile academics. It seems that they themselves don't clearly understand this topic.

[chadwicklin]

"At some point in your life you're probably gonna get the urge to do this" "Don't do this"

This is so hilarious and such a good warnning lol

[LakanBanwa]

Have you considered pairing up with 3blue1brown on a project?

[pradiptahafid]

I cant believe I got this explanation for free.

[owenguo]

Thank you for the amazing videos! They really help a lot with my study in tensor analysis.
There's just one tiny thing I would like to mention about this one, in a textbook about multivariable calculus, the definition of 2-forms is a bit different from that in this video, where you said bilinear forms are sometimes also called 2-forms. The definition given in the textbook also has a condition of anti-symmetry satisfied for 2-forms. So 2-forms are bilinear forms which also satisfy anti-symmetry. Is that a different view for 2-forms?

[portalgunoL]

In other words, metric tensors are bilinear forms that are positive-semidefinite. This also means that they are quadratic forms.

[melmel]

I am from Brazil. My english is bad. Please, enable the subtitle.
Anyway, thank you so much for your excellent classes.