# Definition:Orthogonal (Linear Algebra)/Set

## Definition

Let $\left({V, \left\langle {\cdot} \right\rangle}\right)$ be an inner product space.

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

Then $S$ is an orthogonal set iff its elements are pairwise orthogonal:

$\forall i \ne j: \left\langle {u_i, u_j} \right\rangle = 0$