@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr: a skos:ConceptScheme . psr:-BK1H4W0H-M skos:prefLabel "fonction complexe"@fr, "complex function"@en ; a skos:Concept ; skos:narrower psr:-BXW2PWFS-H . psr:-BXW2PWFS-H skos:definition """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:

{\\\\displaystyle f^{*}(x)=f(-x)}

(where the

{\\\\displaystyle ^{*}}

indicates the complex conjugate) for all

{\\\\displaystyle x}

in the domain of

{\\\\displaystyle f}

. 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

{\\\\displaystyle f}

is a function of two variables it is Hermitian if

{\\\\displaystyle f^{*}(x_{1},x_{2})=f(-x_{1},-x_{2})}

for all pairs

{\\\\displaystyle (x_{1},x_{2})}

in the domain of

{\\\\displaystyle f}

. From this definition it follows immediately that:

{\\\\displaystyle f}

is a Hermitian function if and only if

the real part of ${\\\\displaystyle f}$ is an even function,
the imaginary part of ${\\\\displaystyle f}$ is an odd function.

https://en.wikipedia.org/wiki/Hermitian_function

.