Uploaded March 2019 | Updated September 2026, 2 weeks ago
In this video, I shift the discussion to tensors of rank 2 by defining contravariant, covariant, and mixed tensors of rank 2 via their transformation laws. After laying down these laws (get it?), I clearly describe the notation for a tensor of a particular rank. Specifically, I define a (p,q) tensor as a tensor with a contravariant rank of p (i.e. p indices in the superscript) and covariant rank of q (i.e. q indices in the subscript).
Then, I define the transformation law for a general (p,q) tensor. I finish the video by defining a couple of simple tensor operations: summation, scalar multiplication, and the extension of the two: linear combination.
Questions/requests? Let me know in the comments!
Pre-reqs: The previous videos in the playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/open?id=1EkKWJPxplILIxH4pgHKOVLyk3yMAVIrp
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Anonymous
- Cesar Garza
- Odissei
- Alvin Barnabas
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule
In this video, I shift the discussion to tensors of rank 2 by defining contravariant, covariant, and mixed tensors of rank 2 via their transformation laws. After laying down these laws (get it?), I clearly describe the notation for a tensor of a particular rank. Specifically, I define a (p,q) tensor as a tensor with a contravariant rank of p (i.e. p indices in the superscript) and covariant rank of q (i.e. q indices in the subscript).
Then, I define the transformation law for a general (p,q) tensor. I finish the video by defining a couple of simple tensor operations: summation, scalar multiplication, and the extension of the two: linear combination.
Questions/requests? Let me know in the comments!
Pre-reqs: The previous videos in the playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/open?id=1EkKWJPxplILIxH4pgHKOVLyk3yMAVIrp
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Anonymous
- Cesar Garza
- Odissei
- Alvin Barnabas
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule
