[[Inner product space]]
# Orthonormal set

Let $(V, \mathbb{K}, \braket{ - |-  })$ be an [[inner product space]].
A set $A \sube V$ is said to be **orthonormal** iff its vectors are mutually orthogonal and have norm 1, #m/def/linalg 
i.e. for any $a,b \in A$ 
$$
\begin{align*}
\braket{ a | b } = \delta_{ab} = \begin{cases}
1  & a=b \\
0 & a \neq b
\end{cases}
\end{align*}
$$

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