Two vectors are **orthonormal** if they are orthogonal and their inner product with themself equals $1$.

More formally defined, we picture an inner product space $\mathcal V$ containing a set of $n$ vectors ${v_1, v_2, …, v_n} \in \mathcal V$. This set of vectors is **orthonormal** iff

$$ \forall\ i,j:\langle v_i, v_j\rangle = \delta_{ij}, $$

where $\delta_{ij}$ is the Kronecker delta and $\langle \cdot,\cdot\rangle$ is the inner product defined in $\mathcal V$.