Perturbation results related to palindromic eigenvalue problems

Eric King-wah Chu, Wen-Wei Lin, Chern-Shuh Wang

Abstract


We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic $P(\lambda) \equiv \lambda^2 A_1^T + \lambda A_0 + A_1$, with $A_0,\, A_1 \in \cs^{n \times n}$ and $A_0^T = A_0$. The perturbation of palindromic eigenvalues and eigenvectors, in terms of general matrix polynomials, palindromic linearizations, (semi-Schur) anti-triangular canonical forms and differentiation, are discussed.

doi:10.1017/S144618110800031X

Keywords


anti-triangular form; eigenvalue; eigenvector; matrix polynomial; palindromic eigenvalue problem; palindromic linearization; palindromic pencil; perturbation



DOI: http://dx.doi.org/10.21914/anziamj.v50i0.388



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.