# complementary subspace

## Primary tabs

Defines:
complementary, direct sum, decomposition, orthogonal complement
Synonym:
algebraic complement
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

Regarding the remark following Proposition1: I don’t believe that, given $U$, subspace of $V$, that $U$ has a unique complement in $V$. E.g. any two lines in $\mathbb{R}^{2}$ are complementary. Did I misunderstand something here?