# Homework Help: Tensor property

1. Sep 25, 2010

### typhoonss821

1. The problem statement, all variables and given/known data

Let $$A_{i} , B_{j} , C_{k}$$be vectors.
Is $$A_{1} B_{i} + A_{2} B_{j} + A_{3} B_{k}$$ a tensor?

2. Relevant equations
$$T'_{ijk} = R_{il} R_{jm} R_{kn} T_{ijk}$$

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

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