Perturbation bounds for the joint spectrum of commuting matrices (Q1434382)

Let \(A=(A_1,A_2,\dots,A_m)\) and \(B=(B_1,B_2,\dots,B_m)\) be commuting \(m\)-tuples of \(n\times n\) matrices. The main results establish upper bounds for the distance to the spectrum of \(B\) of an arbitrary \(m\)-tuple \(\lambda\) in the spectrum of \(A\), in terms of a generalized Schur decomposition of \(B\) and certain associated Clifford operators, distinguishing the cases when both \(A\) and \(B\) have real spectra or not.