www.iec.ch

International

Electrotechnical

Commission






Queries, comments, suggestions? Please contact us.



Area Mathematics - Functions / General concepts
IEV ref 103-01-09
en
 weighted inner product
for two complex-valued functions, f _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaamaamaaabaqcLbwaca WGMbaaaaaa@3718@ and g _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaamaamaaabaqcLbwaca WGNbaaaaaa@3719@ , defined on the interval [ a,b] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaamaadmaabaGaamyyai aacYcacaWGIbaacaGLBbGaayzxaaaaaa@39BD@ of ℝ, complex number 〈 f _ , g _ 〉= ∫  a  b f _ (x )  g _ ∗ ​(x) w(x)dx MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaamaabaWaaWaaaeaacaWGMbaaaiaacYcadaadaaqaaiaadEgaaaaacaGLPmIaayPkJaGaeyypa0Zaa8qmaeaadaadaaqaaiaadAgaaaGaaiikaiaadIhaaSqaaiaayIW7caWGHbaabaGaaGjcVlaadkgaa0Gaey4kIipakiaacMcacaaMc8+aaWaaaeaacaWGNbaaamaaCaaaleqabaGaey4fIOcaaOGaaGzaVlaacIcacaWG4bGaaiykaiaaykW7caWG3bGaaiikaiaadIhacaGGPaqcLbuacaGGKbGaamiEaaaa@543B@ , where w(x) is a real function of x called weight
fr
 produit interne pondéré, m
pour deux fonctions à valeurs complexes, f _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaamaamaaabaqcLbwaca WGMbaaaaaa@3718@ et g _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaamaamaaabaqcLbwaca WGNbaaaaaa@3719@ , définies sur l'intervalle [a,b] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeGaciWaamGadaGadeaabaGaaqaaaOqaceaaWGbcdaGae83waS LaciyyaiaacYcacaGGIbGae8xxa0faaa@3A9D@ de ℝ, nombre complexe 〈 f _ , g _ 〉= ∫  a  b f _ (x )  g _ ∗ ​(x) w(x)dx MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaamaabaWaaWaaaeaacaWGMbaaaiaacYcadaadaaqaaiaadEgaaaaacaGLPmIaayPkJaGaeyypa0Zaa8qmaeaadaadaaqaaiaadAgaaaGaaiikaiaadIhaaSqaaiaayIW7caWGHbaabaGaaGjcVlaadkgaa0Gaey4kIipakiaacMcacaaMc8+aaWaaaeaacaWGNbaaamaaCaaaleqabaGaey4fIOcaaOGaaGzaVlaacIcacaWG4bGaaiykaiaaykW7caWG3bGaaiikaiaadIhacaGGPaqcLbuacaGGKbGaamiEaaaa@543B@ , où w(x) est une fonction réelle de x appelée poids
ar
 الضرب الداخلى لمتجهات موزونة
cs
 vážený vnitřní součin
de
 gewichtetes inneres Produkt, n
es
 producto interno ponderado
it
 prodotto pesato interno
ko
 가중 내적
ja
 加重内積
nl
 be gewogen inproduct, n
pl
 iloczyn wewnętrzny ważony
pt
 produto interno ponderado
sr
 пондерисани унутрашњи производ, м јд
sv
 vägd inre produkt
zh
 加权内积
Publication date: 2009-12
Copyright © IEC 2025. All Rights Reserved.