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A set of quantities , whose inner product with an arbitrary vector is a tensor, then prove that the set of quantities is itself a tensor.

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A set of quantities , whose inner product with an arbitrary vector (that is, a contravariant tensor of rank one) is a tensor, then prove that the set of quantities is itself a tensor.

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The solution proves that the set of quantities , whose inner product with an arbitrary vector (that is, a contravariant tensor of rank one) is a tensor, then the set of quantities is itself a tensor. This is mainly for finding the property of the quotient law of tensors.
The solution is given in detail.

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Proof :- Suppose A with upper suffixes mu_1, mu_2, ... , mu_p and lower suffixes
nu_1, ...

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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