Corpus ID: 119150358

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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SHOWING 1-10 OF 42 REFERENCES

A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank

VIEW 3 EXCERPTS

Canonical Structure Transitions of System Pencils

VIEW 2 EXCERPTS

Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils

VIEW 1 EXCERPT