Basic Linear Algebra Concepts for Tensors

In this short video, I go over some very basic concepts in linear algebra that will be relevant to tensors later on in the series. These include Linear Transformations and General Transformations. I finish the video with the Chain Rule for Partial Derivatives (which will also come in handy in the future) expressed in terms of Einstein Notation.

My lecture series on Tensors assumed knowledge of Linear Algebra, so this should be a fairly elementary review for most people. Nonetheless, in my effort to be as self-contained as possible, I made this 'detour' video just in case people needed it. In any case, we have the foundation necessary to tackle the actual Mathematics of Tensors, starting from the next video in the series.

Questions/requests? Let me know in the comments!

Special thanks to my Patrons for supporting me at the $5 level or higher:
- James Mark Wilson
- Cesar Garza
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Elm Mara
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule

[VIGYANACADEMYIGNOU]

YOUR PERFECT IN TEACHING TENSORS BUT YOU TEACH ME ONE MORE THING THAT IS VALUE OF TIME.
WE CAN LEARN A LOT IN SHORT TIME, THANK YOU

[BillPark-eyih]

I really appreciate your videos--clear, intuitive, and concise. I think I found a gem in YouTube.

[yudhisthir]

Hello Sir, Thank you very much for providing this series.

[PunmasterSTP]

Another phenomenal video; thank you so so much for making these!

[account]

Thanks for doing a series on this :) awesomee!

[er]

Good material, great exposition so far, and clear speech. I hope you do not deviate too much from geometric meaning as long as most textbooks do.

[simplephysics]

Great videos, kindly go on in this simple stepped strategy

[eamonnsiocain]

Aside a flagrant abuse of the Subjunctive Mood, a rather clear presentation!

[jacobvandijk]

Well, to be honest, I'm fine ... with an "af-fean" coordinate system ;-)

[yizhang]

Your produnciation of affine confused me.

[amirulhakim]

I am feeling like lost after Einstein's Notation trying to understand this video of yours. I mean, honestly, the explanation is not as good as the previous ones in the series, and I think you only aimed this to the people who already have basic understanding of linear algebra. I am sorry to say that I am disappointed :/