[[Vector basis]]
# Orthonormal basis

In an [[Inner product space]] $(V, \mathbb{K}, \braket{ \cdot | \cdot })$ an **orthonormal basis** is a [[vector basis]] that is an [[Orthonormal set]], #m/def/linalg 
i.e. orthogonal to each other with norm $1$. 
In a countable basis $\{ v_{j} \}_{j \in \mathbb{N}}$ the basis vectors obey the orthogonality relation
$$
\begin{align*}
\braket{ v_{j} | v_{k} } = \delta_{jk}
\end{align*}
$$
where $\delta_{jk}$ is the [[Kronecker delta]].

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#state/tidy | #lang/en | #SemBr