Terán Vergara, Fernando de2021-04-272021-04-272018-07-03De Terán, F. (2018). A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank. SIAM Journal On Matrix Analysis And Applications, 39(3), 1116-1134.0895-4798https://hdl.handle.net/10016/32489The sets of n x n T-palindromic, T-antipalindromic, T-even, and T-odd matrix pencils with rank at most r < n are algebraic subsets of the set of n x n matrix pencils. In this paper, we determine their dimension and we prove that they are all irreducible. This is in contrast with the nonstructured case, since it is known that the set of n x matrix pencils with rank at most r< n is an algebraic set with r + 1 irreducible components. We also show that these sets of structured pencils with bounded rank are the closure of the congruence orbit of a certain structured pencil given in canonical form. This allows us to determine the generic canonical form of a structured n x n matrix pencil with rank at most r, for any of the previous structures.19eng© 2018, Society for Industrial and Applied MathematicsMatrix pencilT-PalindromicT-AlternatingStrict equivalenceCongruenceOrbitSpectral informationAlgebraic setresearch articleMatemáticashttps://doi.org/10.1137/17M1124735open access111631134SIAM Journal on Matrix Analysis and Applications39AR/0000027176