- #1
viciousp
- 51
- 0
Homework Statement
Show that [tex] A \cdot A^{T} [/tex] is symmetric (A is a 2nd order tensor)
Homework Equations
The Attempt at a Solution
So I got down to this and i can see that it will be symmetric however when I try taking the transpose of the solution I can't seem to make it equal the starting equation.
[tex]
\sum_{ij}A_{ij}\delta _{i}\delta _{j}\cdot \sum_{kl}A_{lk}\delta_{k} \delta_{l}=\sum_{ijl}A_{ij}A_{lj}\delta _{i}\delta _{l}
[/tex]
Is there anyway to manipulate the the transpose to make it equal to the original equation or is what I got as far as I can go?
Transpose:
[tex] \sum_{ikl}A_{jl}A_{ji}\delta _{i}\delta _{l} [/tex]
Thanks