First order spectral perturbation theory of square singular matrix pencils (Q929481)

Given a complex square singular pencil \(H(\lambda)= A_0+\lambda A_1\) that has eigenvalues, the paper gives sufficient conditions on \(M(\lambda)= B_0+\lambda B_1\) such that there existsts a first-order eigenvalue perturbation theory for \(H(\lambda)+\varepsilon M(\lambda)\). This result is obtained by restricting the perturbations to a suitable set (namely, by dropping some subset of Lebesgue measure zero) such that the eigenvalues change continuously.