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Chapter 10: Q7P (page 505)

As in problem 6, show that the sum of two 2nd-rank tensors is a 2nd-rank tensor; that the sum of two 4th-rank tensors is a 4th-rank tensor.

Short Answer

Expert verified

Answer

The equation has been proven.

Step by step solution

01

Given Information

The two 2nd-rank tensor and4th- rank tensor.

02

Definition of a cartesian tensor.

The first rank tensor is just a vector. A tensor of the second rank has nine components (in three dimensions) in every rectangular coordinate system.

03

Prove the statement.

Let T and S be the two n-rank tensor.

T+S'i1,i2,..in=T'i1,i2,...in+S'i1,i2,..inT+S'i1,i2,..in=ai1j1...ajnjnTj1...jn+ai1j1....ainjnS'j1jn,..inT+S'i1,i2,..in=T'j1,i1....ainjnT+Sj1....jn

Hence, sum of the two n-rank tensor is n-rank.

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