# subspace

/ˈsəbˌspeɪs/ (US) · /sˈʌbspeɪs/ (UK) · CEFR C1 · Noun

Source: https://englishreference.com/word/subspace
Updated: 2026-05-19

## Definition

a smaller space inside a larger space where the rules of the bigger space still work. In math, it is a set of points that follows the same rules as the whole space.

For teachers: a subset of a vector space that is itself a vector space under the same operations. It must contain the zero vector and be closed under addition and scalar multiplication.

## Examples

- The set of all solutions to this equation forms a subspace.
- In linear algebra, we often look for a subspace that contains only the vectors that satisfy a specific condition.
- The intersection of two subspaces is itself a subspace, provided that the original subspaces are defined over the same field and share the same dimensionality.

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