Definition of complement of a subspace

Created almost 9 years ago, updated about 8 hours ago

A complement of $U\subseteq V$ is a subspace $W$ with $V=U\oplus W$. In finite dimensions, extend a basis of $U$ to a basis of $V$ and let the added vectors span $W$. Complements are usually not unique. In an inner-product space, $U^\perp$ is the distinguished orthogonal complement.

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