Visualization of tensors - part 1

This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor.

Future parts of this series will show more theory and more examples.

It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'tensor' was borrowed with a simplified meaning. In AI it simply means a multi-dimensional array. So for example the array "double a[4][6]" (4 by 6 matrix of doubles) is called a second-order tensor, but there's no special relationship to vector spaces, as shown in the video.

[jamierbb]

Time to get smart on a Thursday morning.

[HitAndMissLab]

This explanation with red and blue spaces is so good.
It takes usually a whole year of studying to reach this level of intuition, and this video does it all in 10 minutes.
Thanks for making the effort!

[sethhhhhhhhhhhhhhh]

This is a wonderful introduction!! This past semester, I took linear algebra and differential equations. Tensors were hiding in the background, as boogeymen that our teacher warned us we would come across later.

Your visualizations were both beautiful and clear. Excited for the rest of the series!! :)

[rockstonic]

cant right now honey, new udiprod about math i dont need to know

[davidgoldgruber]

Best and most compact explanation/visualization of the Cauchy stress tensor I have seen so far. Wish this video had existed a few years ago when I studied the topic at uni.

[Phi]

Finally, a proper explanation in plain English. Been trying to wrap my head around this for over a year now.

[rodrigomunoz]

Thanks! I feel my IQ has increased by 50% in just 10 minutes

[scenemuch]

I've been trying to get a PERFECT understanding of Tensors for decades.... this was Wonderful!

[danielobambelo]

Yes, finally new video, havent even seen it but i know that it will be great, also those who say first are stupid.

[mikip]

Finally!!! Someone in YouTube decides to make the concepto of Tensor easier and meaningful to mortals.

[visualchallenge]

It is amazing what you can learn in 12 minutes ! I have no use for this information but I watched this video in order to get rid of the mystification about this subject that bothered me for more than 30 years. Thank you for this great effort of explanation.

[Assault_Butter_Knife]

Lord almighty what kind of monster have we created?

[natan]

this video is how i know my university meche department has no clue how to teach. in 12 minutes this video explains away most of the gaps from stress analysis because instead of using tensor math we just goofed off with random simplified equations

[rantorakoto]

From the bottom of my heart, thank you 😭❤️ you simply did an amazing work. I've been unsuccessfully trying to understand this for 3 years, I eventually dropped out and just moved forward using tensors without having any idea of what it really is, but now, thanks to you, after 11 minutes, It's finally clear to me, so thank you very much.

[sumairahmad]

Freaking amazing bro. Much appreciated. Can't thank you enough for taking the time out to make this for us!

[あい-wom]

This is the world's easiest explanation of tensors. I wanted to see it when I was a college student over 30 years ago.

[yevgeniygorbachev]

I'm working through the Eigenchris series right now, and I'm really excited to see other math/physics youtubers take a crack at it.

[yousefamar]

as an engineering student those 12 minutes here have more blessing than a 4 month course of my engineering program in university. Just Perfect

[jeremiahvanhook]

Visualization is such a key component of understanding all mathematical concepts. Part 2 PaRt 2 PART 2!!!!

[dialectphilosophy]

Most intuitive and simple explanation of a tensor you can come across on YouTube!