Abstract index notation
Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis. The indices are mere placeholders, not related to any fixed basis and, in particular, are non-numerical. Thus it should not be confused with the Ricci calculus. The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention in order to compensate for the difficulty in describing contractions and covariant differentiation in modern abstract tensor notation, while preserving the explicit covariance of the expressions involved.
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Abstract index notation
Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis. The indices are mere placeholders, not related to any fixed basis and, in particular, are non-numerical. Thus it should not be confused with the Ricci calculus. The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention in order to compensate for the difficulty in describing contractions and covariant differentiation in modern abstract tensor notation, while preserving the explicit covariance of the expressions involved.
has abstract
A notação de índices abstratos ...... ita das expressões envolvidas.
@pt
Abstract index notation is a m ...... f type V and those of type V*.
@en
Die Indexnotation ist eine For ...... die Stufe des Tensors angeben.
@de
La notation en indice abstrait ...... 'écriture du calcul tensoriel.
@fr
抽象指标记号(英语:abstract index notat ...... 和约定类似,但此表示法只是抽象的记号而已,并不表示求和运算。
@zh
抽象添字記法(ちゅうしょうそえじきほう、abstract i ...... 基底(と双対なペア)とは独立なトレース作用素に対応している。
@ja
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A notação de índices abstratos ...... ita das expressões envolvidas.
@pt
Abstract index notation is a m ...... e of the expressions involved.
@en
Die Indexnotation ist eine For ...... von Roger Penrose eingeführt.
@de
La notation en indice abstrait ...... 'écriture du calcul tensoriel.
@fr
抽象指标记号(英语:abstract index notat ...... 和约定类似,但此表示法只是抽象的记号而已,并不表示求和运算。
@zh
抽象添字記法(ちゅうしょうそえじきほう、abstract i ...... としての意味以外の意味を持たない(つまり、数値的ではない)。
@ja
label
Abstract index notation
@en
Indexnotation von Tensoren
@de
Notation en indice abstrait
@fr
Notação de índices abstratos
@pt
抽象指标记号
@zh
抽象添字記法
@ja