Definition:Orthonormal Subset

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

Let $S \subseteq V$ be a subset of $V$.

Then $S$ is an orthonormal subset :


 * $(1): \quad \forall u \in S: \norm u = 1$

where $\norm {\, \cdot \,}$ is the inner product norm.


 * $(2): \quad S$ is an orthogonal set:
 * $\forall u, v \in S: u \ne v \implies \innerprod u v = 0$

Also see

 * Definition:Basis (Hilbert Space)
 * Orthonormal Subset of Hilbert Space Extends to Basis