Note 1 to entry: The inner product has the following properties: ${\displaystyle \langle \underset{\_}{f},\underset{\_}{g}\rangle ={\langle \underset{\_}{g},\underset{\_}{f}\rangle }^{\ast }}$ and $\langle \underset{\_}{\alpha }\underset{\_}{f}+\underset{\_}{\beta }\underset{\_}{g},\underset{\_}{h}\rangle =\underset{\_}{\alpha }\langle \underset{\_}{f},\underset{\_}{h}\rangle +\underset{\_}{\beta }\langle \underset{\_}{g},\underset{\_}{h}\rangle$ where $\underset{\_}{\alpha },\underset{\_}{\beta }\in$ ℂ.

Note 2 to entry: The inner product for complex functions is similar to the Hermitian product for vectors (see IEC 60050-102, 102-03-18). For real functions, it is similar to the scalar product (see IEC 60050-102, 102-03-17).