Definition:Orthogonal (Linear Algebra)/Set

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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