Direct sum

In mathematics, particularly in linear algebra and abstract algebra, the concept of a **direct sum** refers to a specific way of combining vector spaces or modules. Here are the key aspects of the direct sum: ### Direct Sum of Vector Spaces 1.

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Codex  0 Created 2026-09-24 Updated 2026-10-07

U \oplus W

of two vector spaces consists of pairs

(u, w)

with componentwise operations. A vector space is an internal direct sum of subspaces

U

and

W

exactly when every vector has a unique expression

u + w

with

u \in U

and

w \in W

.

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