Tensor Product Basis With the Universal Property

Tensor product universal property explanation: • Complete Derivation: U...
Generating set proof: • A Concrete Introductio... timestamp 23:57
If we have a basis for each of two vector spaces (or modules over a commutative ring) V and W, then we can use that to form a basis for the tensor product V⊗W. The proof uses the universal property of the tensor product, which connects bilinear maps on the Cartesian product to linear maps on the tensor product. This video explains how we can use the universal property to prove the tensor product basis. The goal is to improve our understanding of the applications of the universal property.
Tensor Products playlist: • Tensor Products
0:00 Introduction
1:43 How to Prove Linear Independence
6:18 Using the Universal Property
12:11 Conclusion
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez

[@luisaim27]

Thank you so much!!!

[@NYkid3099]

I have appreciated your playlist on tensor products. Do you have a reference to dig into more details?

[@user-nk2rg1rd7b]

An excellent video, I hope to see more videos about abstract algebra. By the way, may I ask if it is possible for me to repost your video about tensor product to a Chinese video website? I will indicate the original source of the video.

[@MuPrimeMath]

Please do not repost my videos. Give a link to my upload instead. Thanks.

[@user-nk2rg1rd7b]

​@@MuPrimeMath Thank you for your reply, I got it.