- #1

typhoonss821

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## Homework Statement

Let [tex] A_{i} , B_{j} , C_{k}[/tex]be vectors.

Is [tex]A_{1} B_{i} + A_{2} B_{j} + A_{3} B_{k}[/tex] a tensor?

## Homework Equations

[tex]T'_{ijk} = R_{il} R_{jm} R_{kn} T_{ijk} [/tex]

## The Attempt at a Solution

If T is a tensor of rank 3, then [tex]T'_{ijk} = R_{il} R_{jm} R_{kn} T_{ijk} [/tex] where [tex] R^\intercal R =I [/tex]. But I am not sure how to use this relation in the problem. > <

I think it is to use the property of vector [tex]A'_{i} = R_{il} A_{i} [/tex], but difficult appears when I try this way.

Please help...

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