Bilinear form
In mathematics, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:
* B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v)
* B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) The dot product on is an example of a bilinear form. The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.
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Bilinear form
In mathematics, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately:
* B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v)
* B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) The dot product on is an example of a bilinear form. The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms.
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Als Bilinearform bezeichnet ma ...... inearform mit zwei Argumenten.
@de
Bilineární forma je matematick ...... é je lineární v obou složkách.
@cs
Em matemática, sobretudo na ál ...... uma matriz de dimensões n x n.
@pt
En matematiko, dulineara formo ...... ed estas je la alia argumento.
@eo
En matemáticas, una forma bili ...... adas lineales en un argumento.
@es
En mathématiques, plus précisé ...... tique utilise ce cadre formel.
@fr
Forma dwuliniowa albo funkcjon ...... no w artykule o parze dualnej.
@pl
In de wiskunde is een bilineai ...... trix een singuliere matrix is.
@nl
In matematica, più precisament ...... are in entrambe le componenti.
@it
In mathematics, a bilinear for ...... jugate linear in one argument.
@en
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@en
title
Bilinear form
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Unimodular
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wikiPageUsesTemplate
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comment
Als Bilinearform bezeichnet ma ...... inearform mit zwei Argumenten.
@de
Bilineární forma je matematick ...... é je lineární v obou složkách.
@cs
Em matemática, sobretudo na ál ...... uma matriz de dimensões n x n.
@pt
En matematiko, dulineara formo ...... as n×n matrico, aij=B(ei, ej),
@eo
En matemáticas, una forma bili ...... adas lineales en un argumento.
@es
En mathématiques, plus précisé ...... tique utilise ce cadre formel.
@fr
Forma dwuliniowa albo funkcjon ...... óżnionym iloczynem skalarnym).
@pl
In de wiskunde is een bilineai ...... en, geldt voor twee vectoren :
@nl
In matematica, più precisament ...... are in entrambe le componenti.
@it
In mathematics, a bilinear for ...... laced by module homomorphisms.
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label
Bilineaire vorm
@nl
Bilinear form
@en
Bilinearform
@de
Bilineární forma
@cs
Bilinjär form
@sv
Dulineara formo
@eo
Forma bilineal
@ca
Forma bilineal
@es
Forma bilinear
@pt
Forma bilineare
@it