Vector space/Finite dimensional/Linear subspace/Direct complement/Fact

Let ${}V$ be a finite-dimensional ${}K$-vector space, and let ${}U\subseteq V$ be a linear subspace.

Then there exists a linear subspace

${}W\subseteq V$ such that we have the direct sum decomposition

${}V=U\oplus W\,.$

Proof, Write another proof