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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Tensor with complex eigenvalues

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