Category:Examples of Orthonormal Subsets

From ProofWiki
Jump to navigation Jump to search

This category contains examples of Orthonormal Subset.

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 (of $V$) if and only if:

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

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

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

Pages in category "Examples of Orthonormal Subsets"

The following 2 pages are in this category, out of 2 total.