# Definition:Orthonormal Basis

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 It has been suggested that this page or section be merged into Definition:Orthonormal Basis of Vector Space. (Discuss)

## Definition

Let $\mathbb F$ be a field.

Let $V$ be a vector space over $\mathbb F$.

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

Then $S$ is an orthonormal basis if and only if:

$(1): \quad S$ is a basis.
$(2): \quad S$ is orthonormal.