A general framework is presented for analyzing the continuous evolution of eigendecompositions of matrices. More specifically, for arbitrary operator norms, a general framework based on pseudospectraâ€¦ (More)

Let A be a matrix with distinct eigenvalues and let w(A) be the distance from A to the set of defective matrices (using either the 2norm or the Frobenius norm). Define Î› , the -pseudospectrum of A,â€¦ (More)

We consider the normwise condition number and backward error of eigenvalues of matrix polynomials having â‹†-palindromic/antipalindromic and â‹†-even/odd structure with respect to structure preservingâ€¦ (More)

We investigate the effect of linear perturbations on several structured matrix pencils arising in control theory. These include skew-symmetric/symmetric pencils arising in the computation of optimalâ€¦ (More)

Motivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimalâ€¦ (More)

We derive a formula for the backward error of a complex number Î» when considered as an approximate eigenvalue of a Hermitian matrix pencil or polynomial with respect to Hermitian perturbations. Theâ€¦ (More)

We derive formulas for the backward error of an approximate eigenvalue of a âˆ—palindromic matrix polynomial with respect to âˆ—-palindromic perturbations. Such formulas are also obtained for complex Tâ€¦ (More)