1
vote
2answers
22 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 ...
8
votes
2answers
611 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 ...