Direct-sum complement
= Direct-sum complement
For every subspace $U$ of a finite-dimensional vector space $V$, extending a basis of $U$ to a basis of $V$ produces a subspace $W$ such that $V=U\oplus W$.
= Direct-sum complement
For every subspace $U$ of a finite-dimensional vector space $V$, extending a basis of $U$ to a basis of $V$ produces a subspace $W$ such that $V=U\oplus W$.