Symmetric traceless tensor

kaksmet

Hi everybody,

With the use of two vectors $v^i$ and $v^i$, and $\delta^{ij}$, how can I construct two linearly independent rank 2 basis tensors which are symmetric and traceless? (i,j running over 1-2)

Any symmetric traceless 2x2 matrix can be written as a linear combination of diag(1,-1) and offdiag(1,1), but how can I construct a basis with the given set of vectors and tensors above?

Thanks for taking the time to read and I hope I made myself clear enough.

Cheers