Definition:Complementary Subspace

Definition
Let $X$ be a vector space.

Let $N, Y \subseteq X$ be subspaces.

Then $Y$ is a complementary subspace of $N$ $X$ is the direct sum:
 * $X = N \oplus Y$

That is, for each $x \in X$, there exist unique $n \in N$ and $y \in Y$ such that:
 * $x = n + y$

Also see

 * Existence of Complementary Subspace