Perturbation analysis for the eigenvalue problem of a formal product of matrices (Q1599133)

A perturbation theory is given for generalized deflating subspaces and eigenvalues of a formal matrix product. The theory generalizes the classical perturbation results for matrices and matrix pencils. The perturbation bounds can be used to estimate the errors of the generalized deflating subspaces and eigenvalues when they are computed by the periodic \(QR\) or \(QZ\) algorithms. As an application the perturbation theory for Hamiltonian pencils is studied. All results are presented for complex matrices.