Publication: A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank
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2018-07-03
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Society for Industrial and Applied Mathematics (SIAM)
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Abstract
The 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.
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Matrix pencil, T-Palindromic, T-Alternating, Strict equivalence, Congruence, Orbit, Spectral information, Algebraic set
Bibliographic citation
De 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.