If the vector (which you write as a column vector) has components , then is the matrix product of with the transpose of . It is a 3×3 matrix with components To get the matrix you then have to divide each element by

I'm no engineer, but I'm guessing that the compressive part corresponds to negative eigenvalues and the tensile part to positive eigenvalues (or maybe the other way round). Say there is one positive eigenvalue, with eigenvector , and two negative eigenvalues, with eigenvectors and . Then my guess is that the stress matrix needs to be decomposed into the positive part which would be , and the negative part which is .