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## Homework Statement

We have the following orthogonal tensor in R

^{3}:

[itex] t_{ij} (x^2) = a (x^2) x_i x_j + b(x^2) \delta _{ij} x^2 + c(x^2) \epsilon_ {ijk} x_k [/itex]

Calculate the following quantities and simplify your expression as much as possible:

[itex] \nabla _j t_{ij}(x)[/itex]

and

[itex] \epsilon _{ijk} \nabla _i t_{jk}(x) = 0 [/itex]

and

[itex] \epsilon _{ijk} \nabla _i t_{jk}(x) = 0 [/itex]

## Homework Equations

The equations given in my book are:

[itex] (\nabla f)_i = \Lambda _{ji} \frac{\partial f}{\partial x_j} [/itex] ( with a tilda on the last x

_{j}

[itex] \nabla _i = \Lambda_i^j \nabla _j [/itex] (with a tilda "~" on the last nabla)

## The Attempt at a Solution

My problem is that these equations that I have are all assuming that you have a tensor in the form of a matrix, but this is not the case I believe. Also in the book leading up to these equations you have a vector

**x**which is dependent on x

_{i}and on

**e**

_{i}. Which is now also not the case. Only the first term with a is dependent on x

_{i}or x

_{j}, but I can't imagine that the rest of the function just falls away..