- #1
peripatein
- 880
- 0
Hi,
Given that Aij is a contravariant tensor of rank 2, is the following a contravariant tensor of rank 3: Aijxi/xk?
Using the chain rule, I have found xi/xk to be a contravariant tensor of rank 1:
[itex]\bar{x}[/itex]i/[itex]\bar{x}[/itex]k = [itex]\bar{x}[/itex]i/xl * xl/[itex]\bar{x}[/itex]k
Is that correct? Does the above product indeed yield a contravariant tensor of rank 3?
Homework Statement
Given that Aij is a contravariant tensor of rank 2, is the following a contravariant tensor of rank 3: Aijxi/xk?
The Attempt at a Solution
Using the chain rule, I have found xi/xk to be a contravariant tensor of rank 1:
[itex]\bar{x}[/itex]i/[itex]\bar{x}[/itex]k = [itex]\bar{x}[/itex]i/xl * xl/[itex]\bar{x}[/itex]k
Is that correct? Does the above product indeed yield a contravariant tensor of rank 3?