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#* It is emphasized that this definition depends on the scalar field <math>\mathbb{F}</math> underlying the ___domain <math>X.</math>
#* This property is used in the definition of [[linear functional]]s and [[linear map]]s.{{sfn|Kubrusly|2011|p=200}}
#{{em|[[Semilinear map|{{visible anchor|Conjugate homogeneity|Conjugate homogeneous}}]]}}:{{sfn|Kubrusly|2011|p=310}} <math>f(sx) = \overline{s} f(x)</math> for all <math>x \in X</math> and all scalars <math>s \in \mathbb{F}.</math>
#* If <math>\mathbb{F} = \Complex</math> then <math>\overline{s}</math> typically denotes the [[complex conjugate]] of <math>s</math>. But more generally, as with [[semilinear map]]s for example, <math>\overline{s}</math> could be the image of <math>s</math> under some distinguished automorphism of <math>\mathbb{F}.</math>
#* Along with [[Additive map|additivity]], this property is assumed in the definition of an [[antilinear map]]. It is also assumed that one of the two coordinates of a [[sesquilinear form]] has this property (such as the [[inner product]] of a [[Hilbert space]]).
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