Uploaded December 2024 | Updated September 2026, 2 weeks ago
The foil to regular vectors in Tensor Analysis: dual vectors (a.k.a. covectors, one-forms) are best thought of as functions that operate on regular vectors. This video defines dual vectors (starting with the more general abstract definition followed by the tensor algebra definition) and then gives some intuition behind what dual vectors represent.
Questions/requests? Let me know in the comments!
Pre-reqs: Previous videos in this playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/file/d/1Y-2hpP6RkOfX7najQkXx45B-_jEOhkyC/view?usp=drive_link
Special thanks to my Patrons:
Matthew
Patapom
Eugene Bulkin
Andy Johnston
Lina Stritt
Patrick Gibson
Joseph Dubeau
The foil to regular vectors in Tensor Analysis: dual vectors (a.k.a. covectors, one-forms) are best thought of as functions that operate on regular vectors. This video defines dual vectors (starting with the more general abstract definition followed by the tensor algebra definition) and then gives some intuition behind what dual vectors represent.
Questions/requests? Let me know in the comments!
Pre-reqs: Previous videos in this playlist - youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: drive.google.com/file/d/1Y-2hpP6RkOfX7najQkXx45B-_jEOhkyC/view?usp=drive_link
Special thanks to my Patrons:
Matthew
Patapom
Eugene Bulkin
Andy Johnston
Lina Stritt
Patrick Gibson
Joseph Dubeau









