On Householder sets for matrix polynomials

We present a generalization of Householder sets for matrix polynomials. After defining these sets, we analyze their topological and algebraic properties, which include containing all of the eigenvalues of a given matrix polynomial. Then, we use instances of these sets to derive the Geršgorin set, weighted Geršgorin set, and weighted pseudospectra of a matrix polynomial. Finally, we show that Householder sets are intimately connected to the Bauer-Fike theorem by using these sets to derive Bauer-Fike-type bounds for matrix polynomials.

© This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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Work Title On Householder sets for matrix polynomials
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Open Access
Creators
  1. Thomas R. Cameron
  2. Panayiotis J. Psarrakos
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Elsevier BV
Publication Date January 2020
Publisher Identifier (DOI)
  1. 10.1016/j.laa.2019.09.037
Source
  1. Linear Algebra and its Applications
Deposited September 09, 2021

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