Uploaded September 2021 | Updated September 2026, 2 weeks ago
The tensor product of vector spaces (or modules over a ring) can be difficult to understand at first because it's not obvious how calculations can be done with the elements of a tensor product. In this video we give an explanation of an explicit construction of the tensor product and work through several example computations, such as finding a generating set.
Learning Linear Algebra playlist: youtube.com/playlist?list=PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs
Tensor Products playlist: youtube.com/playlist?list=PLug5ZIRrShJHCtzgzZyRqSdzr8wYlN2qk
0:00 Construction
14:01 Examples
23:33 Basis for Tensor Product
28:44 Examples
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Music: C418 - Pr Department
The tensor product of vector spaces (or modules over a ring) can be difficult to understand at first because it's not obvious how calculations can be done with the elements of a tensor product. In this video we give an explanation of an explicit construction of the tensor product and work through several example computations, such as finding a generating set.
Learning Linear Algebra playlist: youtube.com/playlist?list=PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs
Tensor Products playlist: youtube.com/playlist?list=PLug5ZIRrShJHCtzgzZyRqSdzr8wYlN2qk
0:00 Construction
14:01 Examples
23:33 Basis for Tensor Product
28:44 Examples
Subscribe to see more new math videos!
Music: C418 - Pr Department
![I Want to Play a Game: Proving [0,1] is Uncountable](https://i.ytimg.com/vi/Mcfnnp8rxkI/mqdefault.jpg "I Want to Play a Game: Proving [0,1] is Uncountable
The interval [0,1] is uncountable, and there are many ways to prove that. Cantors diagonal argument is a classic example. But theres another way: proof by playing a game. This video is an explanation of a proof by contradiction after assuming that the infinite set [0,1] is countable and playing a game on that interval. All we need is basic calculus for the limits of sequences!
Original based on Grossman & Turett: https://arxiv.org/pdf/math/0606253
Calculus Problems playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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Music: C418 - Smooth Fall")
