Tensor Product Basis With the Universal Property

Tensor product universal property explanation: /watch/QY_CLdhZzZvZC Generating set proof: /watch/7341=t?47_dnjBZSnKZ1 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: /playlist/PLug5ZIRrShJHCtzgzZyRqSdzr8wYlN2qk 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

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