Hermitian function
In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: (where the formula_2 indicates the complex conjugate) for all formula_3 in the domain of formula_4. In physics, this property is referred to as PT symmetry. This definition extends also to functions of two or more variables, e.g., in the case that formula_4 is a function of two variables it is Hermitian if for all pairs formula_7 in the domain of formula_4. From this definition it follows immediately that: formula_4  is a Hermitian function if and only if Motivation. Hermitian functions appear frequently in mathematics, physics, and signal processing. For example, the following two statements follow from basic properties of the Fourier transform: Since the Fourier transform of a real signal is guaranteed to be Hermitian, it can be compressed using the Hermitian even/odd symmetry. This, for example, allows the discrete Fourier transform of a signal (which is in general complex) to be stored in the same space as the original real signal. Where the formula_17 is cross-correlation, and formula_18 is convolution.