Orthonormality

linear-algebra

Definition

Orthonormality

A family of vectors $\{e_i{\}}_{i\in I}$ in an inner product space is orthonormal if

$$⟨e_i|e_j⟩={\delta }_{ij}$$

where ${\delta }_{ij}$ is the Kronecker delta. Equivalently,

• $⟨e_i|e_j⟩=0$ for $i\ne j$ (orthogonality), and
• $⟨e_i|e_i⟩=1$ for all $i$ (normalisation).