I'm currently researching a 3d tensor, where certain combinations of terms can cause the principal values (eigenvalues) to become complex. This would then seem to imply that the associated eigenvectors would also become complex. What now, if this tensor were part of a larger equation, ultimately solved in expanded form (3d), using numerical methods? What could we reasonably expect to occur? Would a real solution be obtained, or would the numerics crash against the complex solutions. If now, this tensor is dotted against a vector in such a way that the inner workings of the tensor are hidden in the detail of the expanded pde form, & the new equation is solved using numerical methods? What could we reasonably expect to occur? In the second form, in a few simulations I have to hand, in the final computed result field, computation of the eigenvalues shows up as real, or complex & in very distinct regions - so there is a carry-through, only it is not obvious in the fully-expanded 3d form. There is a very sound reason behind the questions I'm asking, as it applies to a few rather well-known pde equations. I'd love to know if this hurdle has been addressed in the past & if so, a few links would be gratefully appreciated.