# Generic symmetric matrix pencils with bounded rank.

@inproceedings{Tern2018GenericSM, title={Generic symmetric matrix pencils with bounded rank.}, author={Fernando de Ter{\'a}n and Andrii Dmytryshyn and Froil'an M. Dopico}, year={2018} }

We show that the set of $n \times n$ complex symmetric matrix pencils of rank at most $r$ is the union of the closures of $\lfloor r/2\rfloor +1$ sets of matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of $n \times n$ complex symmetric matrix pencils of rank at most $r$. We also show that these closures correspond to the irreducible components of the set of $n\times n$ symmetric matrix pencils with rank… CONTINUE READING

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## Generic symmetric matrix polynomials with bounded rank and fixed odd grade

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