A note on eigenvalues of fixed rank perturbations of diagonal matrices
Wayne W. Barrett, Dale D. Olesky, Pauline Van den Driessche · Linear and Multilinear Algebra · 1991
An n × n real matrix T ∈ Mk if T=D+A where D is diagonal and rank.A= k. For 0 ≤ k ≤ n − 1 and A diagonally symmetrizable, we prove that all but k eigenvalues of T lie in the closed interval between the minimum and maximum diagonal entry of D, but show that no such result holds for general A. This answers an open problem posed by Furth and Sierksma. We also correct their proof of the result that .