1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector to Tensor properties

  1. Apr 5, 2016 #1
    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. jcsd
  3. Apr 5, 2016 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Well, how do the vectors ##A## and ##B## transform under rotations?
     
  4. Apr 6, 2016 #3
    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?
     
  5. Apr 6, 2016 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, something is a tensor if it transforms like a tensor.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Vector to Tensor properties
Loading...