Tensor Calculus Made Simple by Taha Sochi

Author:Taha Sochi [Sochi, Taha]
Language: eng
Format: azw3
Publisher: CreateSpace
Published: 2017-01-31T16:00:00+00:00

3.1  Addition and Subtraction

Tensors of the same rank and type (see Footnote 43 in § 8↓) can be added algebraically to produce a tensor of the same rank and type, e.g. a = b + c

Ai = Bi − Ci

Aij = Bij + Cij

The added/subtracted terms should have the same indicial structure with regard to their free indices, as explained in § 2.3↑; hence Aijk and Bjik cannot be added or subtracted although they are of the same rank and type, but Amimjk and Bijk can be added and subtracted. Addition of tensors is associative and commutative, that is (see Footnote 44 in § 8↓): (95) (A + B) + C = A + (B + C)

(96) A + B = B + A

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