Is A_{i.j} - A_{j.i} a Tensor Under Non-Linear Transformations?

[JohanL]

prove that for any vector

$$A_i$$

the expression

$$A_{i.j}-A_{j.i}$$

is a tensor, even under non-linear transformations. Similarly prove that for any antisymmetric tensor

$$E_{ij}$$

the expression

$$E_{ij.k}+E_{jk.i}+E_{ki.j}$$

is a tensor.

____________________________

What does the dots mean?
For example between i and j in i.j ?

 

[dextercioby]

Partial derivatives.

Daniel.

 

[JohanL]

Thanks.
I solved the problem except that about
even under non-linear transformations.
non-linear transformations from one set of coordinates to another?
what changes if its non-linear transformations?

 

[Daverz]

Maybe non-linear means higher order terms in partials derivitives of the coordinates? They would cancel out in the examples given.