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Chapter 10: Q9P (page 505)

XiAij=Bj.

Short Answer

Expert verified

Answer

The equation has been proven.

Step by step solution

01

Given Information

The tensorXiAij=Bj.

01

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.

02

Prove that X is a tensor.

Let XiAij=Biwhere B is a non-zero tensor.

Apply transformation law on A and B.

0=X'伪A'伪尾-a尾iB'尾0=X'伪A'伪尾-a尾iXiAij0=X'伪A'伪尾-a尾ja伪ia纬iXiA'伪纬0=X'伪A'伪尾-未尾ja伪iXiA'伪纬0=X'伪-a伪iXiA'伪尾

Let S伪=X'伪-a伪iXiA'伪尾

Hence, STA=0

The equation mentioned above is true for any matrix A.

Thus, X is a tensor.

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Most popular questions from this chapter

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