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 $W$ if and only if:

$V = U \oplus W$, 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)

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.