# Homework Help: Vector to Tensor properties

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1. Apr 5, 2016

### flintbox

1. The problem statement, all variables and given/known data
Suppose A and B are vectors. Show that the object Q with nine components Qij=AiBj is a tensor of rank 2.

2. Relevant equations
A tensor transforms under rotations (R) as a vector:
Tij'=RinRjmTnm

3. The attempt at a solution
I wanted to just create the matrix, but I don't know how to prove that this is also a tensor.

2. Apr 5, 2016

### Dick

Well, how do the vectors $A$ and $B$ transform under rotations?

3. Apr 6, 2016

### flintbox

Thanks a lot!
I think I understand it now:
$$A_i' B_j' = R_{in}A_n R_{jm}A_m$$
$$A_i' B_j' = R_{in} R_{jm} (A_n A_m)$$
$$A_i' B_j' = R_{in} R_{jm} Q_{nm}$$
$$A_i' B_j' = Q'_{nm}$$
So we for proving something is a tensor, we just apply some transformations to it, right?

4. Apr 6, 2016

### Dick

Yes, something is a tensor if it transforms like a tensor.