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Tensor Algebra

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Abstract

The set \(E^{*}\) of all linear forms on E becomes a vector space on \(\mathfrak {R}\) when we define the sum of two linear forms \(\varvec{\omega }\), \(\varvec{\sigma }\in E^{*}\) and the product of the scalar \(a\in \mathfrak {R}\) and the linear form \(\varvec{\omega }\) in the following way.

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Change history

  • 21 November 2019

    Extra supplementary Material was added to Chapter one titled “Tensor Algebra”.

Notes

  1. 1.

    For the contents of Chaps. 14, see [3, 22, 35, 36, 57].

  2. 2.

    Here \(\delta ^{i}_{j}\) is the Kronecker symbol

    $$ \delta ^{i}_{j}= {\left\{ \begin{array}{ll} 0, &{}i\ne j, \\ 1, &{}i= j. \end{array}\right. } $$

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Correspondence to Antonio Romano .

1 Electronic supplementary material

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Supplementary material 1 (nb 392 KB)

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Romano, A., Mango Furnari, M. (2019). Tensor Algebra. In: The Physical and Mathematical Foundations of the Theory of Relativity. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27237-1_1

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