I have a 3D spherical distribution in polar co-ordinates. The directional cosines of any point in the distribution are l, m and n. From which a matrix, T, is constructed (shown below) using the idea of moments.

My question is T a tensor? If so how would I proove this? Invariants?

(sorry if this should be in linear algebra, I couldnt decide, please move it if more appropriate)
Directional statistics and tensors....-dir_cosines.png