0
votes
0answers
121 views

How to prove that the Kronecker delta is the unique isotropic tensor of order 2?

Is there a way to prove that the Kronecker delta $\delta_{ij}$ is indeed the only isotropic second order tensor (i.e. invariant under rotation), i.e. so we can write $T_{ij} = \lambda \delta_{ij}$ ...
1
vote
2answers
29 views

Rotation invariance of higher than 2 dimensions

According to this $f_2(x_1,x_2) = x_1^2 + x_2^2$ is invariant under rotation. I wanted to ask if a function $f_n(x_1,x_2,...,x_n) = x_1^2 + x_2^2 + ...+ x_n^2$ is also rotation invariant. In other ...
9
votes
2answers
779 views

Rotation invariant tensors

It is often claimed that the only tensors invariant under the orthogonal transformations (rotations) are the Kronecker delta $\delta_{ij}$, the Levi-Civita epsilon $\epsilon_{ijk}$ and various ...