---
tag: 0BF2DE2SYK
kind: concept
name: Tensor product of vector spaces
msc: [15A69]
sources:
  - url: https://en.wikipedia.org/wiki/Tensor_product
    locator: As a quotient space
same_as:
  wikidata: Q1163016
  wikipedia: Tensor product
---

## Summary

The tensor product of two vector spaces is a vector space spanned by symbols $v \otimes w$.
These symbols are bilinear in $v$ and $w$, and no other relations hold.