# Change of basis for deviatoric second order tensors

Dear mechanicians

I remember reading somewhere that someone had a proof of the following:
Given a deviatoric/traceless second order tensor it is possible to find a basis for which all the normal/direct components equal zero.
For 2d this is easy: a basis rotated 45deg wrt. the eigenbasis.
The proof concerned 3d and it may have been Gurtin that had it in one of his books (sometihng tells me "The Linear Theory of Elasticity" (1972) as I don't have access to this one), but I'm not certain.

Can anyone help me in this matter?

-Espen

### Re: Change of basis for deviatoric second order tensors

Not sure about a rigorous proof but you could try starting with a spectral decomposition of the tensor, compute the orthogonal complements of the eigenbasis, and express the tensor in the new basis.  See, e.g., http://math.stackexchange.com/questions/392466/orthogonal-complement-of-the-diagonal-matrices-in-the-inner-product-space-of-mat?rq=1

-- Biswajit