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Generic symmetric matrix pencils with bounded rank

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URI: https://hdl.handle.net/10016/32292
ISSN: 1664-039X
DOI: https://doi.org/10.4171/jst/316
UXXI: AR/0000027032
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Generic_JST_2020_ps.pdf (435.93 KB)
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2020-09-15
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European Mathematical Society (EMS)
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Abstract
We 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.
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Matrix pencil, Symmetric pencil, Strict equivalence, Congruence, Orbit, Bundle, Spectral information, Complete eigenstructure
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De Terán, F., Dmytryshyn, A. & Dopico, F. (2020). Generic symmetric matrix pencils with bounded rank. Journal of Spectral Theory, 10(3), pp. 905–926.
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