---
tag: 0S7W6EG32V
kind: concept
name: External direct sum
msc: [15A03, 16D10]
sources:
  - url: https://en.wikipedia.org/wiki/Direct_sum_of_modules
    locator: Construction for two vector spaces
---

## Summary

The external direct sum of a family of vector spaces is the space of families of vectors, one vector from each space.
Only finitely many entries of such a family are nonzero.
For finitely many spaces it is the product of the spaces.