Definition:Complementary Subspace
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Definition
Let $X$ be a vector space.
Let $N, Y \subseteq X$ be subspaces.
Then $Y$ is a complementary subspace of $N$ if and only if $X$ is the direct sum:
- $X = N \oplus Y$
That is, if and only if for each $x \in X$, there exist unique $n \in N$ and $y \in Y$ such that:
- $x = n + y$
Also see
Sources
- 2002: Peter D. Lax: Functional Analysis: $2.2$: Index of a Linear Map