Terán Vergara, Fernando deDmytryshyn, AndriiMartínez Dopico, Froilán César2021-04-072021-04-072020-09-15De Terán, F., Dmytryshyn, A. & Dopico, F. (2020). Generic symmetric matrix pencils with bounded rank. Journal of Spectral Theory, 10(3), pp. 905–926.1664-039Xhttps://hdl.handle.net/10016/32292We show that the set of n × n complex symmetric matrix pencils of rank at most r is the union of the closures of [r/2] + 1 sets of matrix pencils with some, explicitly described,complete eigenstructures. As a consequence, these are the generic complete eigenstructures of n × n complex symmetric matrix pencils of rank at most r. We also show that these closures correspondto the irreducible components of the set of n × n symmetric matrix pencils with rank at most r when considered as an algebraic set.22eng© 2021 EMS Publishing House.Matrix pencilSymmetric pencilStrict equivalenceCongruenceOrbitBundleSpectral informationComplete eigenstructureresearch articleMatemáticashttps://doi.org/10.4171/jst/316open access9053926Journal of Spectral Theory10AR/0000027032