---
tag: 0XYYT5KNTX
kind: concept
name: Direct sum of subspaces
aliases: [internal-direct-sum]
msc: [15A03]
sources:
  - url: https://en.wikipedia.org/wiki/Direct_sum_of_modules
    locator: Internal direct sum
---

## Summary

A vector space is the direct sum of a family of subspaces when each vector is a sum of vectors from the subspaces.
This sum must be unique.