Generic low rank perturbations of structured regular matrix pencils and structured matrices

Batzke, Leonhard

doi:10.14279/depositonce-4776

2015

DOI: 10.14279/depositonce-4776

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Generic low rank perturbations of structured regular matrix pencils and structured matrices

Leonhard Batzke¹

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Cited by 2 publications

References 73 publications

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

Terán¹

2018

SIAM J. Matrix Anal. & Appl.

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The sets of n × n-palindromic,-anti-palindromic,-even, and-odd matrix pencils with rank at most r < n are algebraic subsets of the set of n × n matrix pencils. In this paper, we determine their dimension and we prove that they are all irreducible. This is in contrast with the non-structured case, since it is known that the set of n × n 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 × n matrix pencil with rank at most r, for any of the previous structures.

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

Terán¹

2018

SIAM J. Matrix Anal. & Appl.

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Low Rank Perturbations of Quaternion Matrices

Mehl

Ran

2017

ELA

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Dedicated to the memory of Leiba Rodman, whose work inspired us greatly.Abstract. Low rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices it is well known that under a generic rank-k perturbation the k largest Jordan blocks of a given eigenvalue will disappear while additional smaller Jordan blocks will remain. In this paper, it is shown that the same is true for real eigenvalues of quaternion matrices, but for complex nonreal eigenvalues the situation is different: not only the largest k, but the largest 2k Jordan blocks of a given eigenvalue will disappear under generic quaternion perturbations of rank k. Special emphasis is also given to Hermitian and skew-Hermitian quaternion matrices and generic low rank perturbations that are structure-preserving.

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Generic low rank perturbations of structured regular matrix pencils and structured matrices

Cited by 2 publications

References 73 publications

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

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

Low Rank Perturbations of Quaternion Matrices

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