On the simple shear decompositions of a deviator (Q800116)

The author gives an alternative proof (see the author [Q. Appl. Math. 41, 119--123 (1983; Zbl 0523.73016)]) of the following decomposition theorem: Let \(D\) be a deviator (in a 3-dimensional inner product space), i.e. a symmetric tensor with \(\text{tr}\, D=0\). Then there is an orthonormal basis \(\{u,v,w\}\) such that \(D\) admits the decomposition \[ D=a(u\otimes v+v\otimes u)+b(v\otimes w+w\otimes v)+c(w\otimes u+u\otimes w), \] where \(a,b,c\in \mathbb R\). He shows that the orthonormal basis with respect to which \(D\) admits the decomposition described above is not unique.