---
tag: 0EX2HPXPJ6
kind: concept
name: Product of vector spaces
msc: [15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Direct_sum_of_modules
    locator: Construction for two vector spaces
---

## Summary

The product of two vector spaces over the same field is the set of pairs, with addition and scalar multiplication done in each component.