Perturbation results related to palindromic eigenvalue problems

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