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A Structured Kronecker form for the Palindromic Eigenvalue Problem
Author(s) -
Schröder Christian
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610341
Subject(s) - kronecker delta , eigenvalues and eigenvectors , palindrome , pencil (optics) , matrix pencil , mathematics , canonical form , set (abstract data type) , characterization (materials science) , combinatorics , algebra over a field , pure mathematics , computer science , physics , chemistry , biochemistry , quantum mechanics , crispr , gene , programming language , optics
We consider a structured generalized eigenvalue problem of the form Ax = λ (– A T ) x , called palindromic eigenvalue problem. We will explain this name and give applications. To characterize the spectral properties of this problem we introduce a structured version of the Kronecker canonical form. As an application we present a characterization of the set of pencils B + λC that are equivalent to a palindromic pencil A + λA T . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)