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.

12:49 Wednesday 26 May 2021