On Householder sets for matrix polynomials

Thomas R. Cameron, Panayiotis J. Psarrakos

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)105-126
Number of pages22
JournalLinear Algebra and Its Applications
StatePublished - Jan 15 2020

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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