Definition:Orthogonal (Linear Algebra)/Set

Definition

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

Let $S = \set {u_1, \ldots, u_n}$ be a subset of $V$.

Then $S$ is an orthogonal set if and only if its elements are pairwise orthogonal:

$\forall i \ne j: \innerprod {u_i} {u_j} = 0$

Also see

• Definition:Orthonormal (Linear Algebra)