Definition:Orthogonal (Linear Algebra)/Sets

Definition
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space. Let $A, B \subseteq V$.

We say that $A$ and $B$ are orthogonal :


 * $\forall a \in A, b \in B: a \perp b$

That is, if $a$ and $b$ are orthogonal elements of $A$ and $B$ for all $a \in A$ and $b \in B$.

We write:


 * $A \perp B$

Also denoted as
In the case where $A = \set a$ is a singleton, the notation $a \perp B$ is often encountered.