\begin{definition}[Definition:Internal Orthogonal Sum (Bilinear Space)]
Let $\mathbb K$ be a field.
Let $\left({V, f}\right)$ be a reflexive bilinear space over $\mathbb K$.
Let $U, W \subset V$ be subspaces of $V$.
Then $V$ is the '''internal orthogonal (direct) sum''' of $U$ and $W$ {{iff}}:
:$V = U \oplus W$, that is, $V$ is the internal direct sum of $U$ and $W$
:$U \perp W$, that is, $U$ and $W$ are orthogonal.
This is denoted: $V = U\oplus W$.
\end{definition}