Annali di Matematica Pura ed Applicata

, Volume 68, Issue 1, pp 45–50 | Cite as

On tensors which are functions of vectors

  • N. D. Sen Gupta


It has been shown that the most general constant tensor of any rank is the possible algebraic combination of Kronecker tensor Open image in new window and the totally antisymmetric tensor\(\varepsilon _{\mu _1 \mu _2 \ldots \mu _n } \) ... μn. Further, the tensor of a given rank r, which are functions of vectors p's, are suitable algebraic combinations of the tensor\(p_{i_1 }^1 p_{i_2 }^2 \ldots p_{i_r }^r \) and the two constant tensors with coefficients which are functions of the scalar products formed by the vectors.


Scalar Product Constant Tensor Algebraic Combination 
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  1. (1) (i).
    G. Zin,Funzioni tensoriali di un vettore e leggi dell'elettromagnetismo, Ann. di Mat. Pura e App. (Volume dedicated to ProfessorAntonio Signorini) 1960 (IV), Vol. L, pp. 341–378.MathSciNetGoogle Scholar
  2. (1) (ii).
    Su una particolare classe di funzioni tensoriali di un tetravettore e sulla conseguente interpretazione dell'elettromagnetismo di Maxwell-Lorentz, ibid 1963 (IV). Vol. LXI, pp. 351–383.Google Scholar
  3. (2).
    See footnote (1).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1965

Authors and Affiliations

  • N. D. Sen Gupta
    • 1
  1. 1.Tata Institute of Fundamental Research, ColabaBombay 5India

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