Definition:Internal Orthogonal Sum (Bilinear Space)

Definition
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 $W$ :
 * $V = U \oplus W$, 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: $V = U\oplus W$.

Also denoted as
The internal orthogonal sum is also denoted with a $\perp$ inside a $\bigcirc$, but this symbol is not included as standard in $\LaTeX$.

Also see

 * Definition:Orthogonal Sum (Bilinear Space)