On Householder sets for matrix polynomials
作者： Thomas R. Cameron , Panayiotis J. Psarrakos
DOI: 10.1016/J.LAA.2019.09.037
关键词: Set (abstract data type) 、 Algebraic properties 、 Generalization 、 Matrix polynomial 、 Mathematics 、 Eigenvalues and eigenvectors 、 Combinatorics 、 Matrix (mathematics)
摘要: Abstract 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 the eigenvalues given polynomial. Then, use instances to derive Gersgorin set, weighted pseudospectra Finally, show that are intimately connected Bauer-Fike theorem by using Bauer-Fike-type bounds
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