2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116590We prove conditions for equality between the extreme eigenvalues of a matrix and its quotient. In particular, we give a lower bound on the largest singular value of a matrix and generalize a result of Finck and Grohmann about the largest eigenvalue of a graph.CombinatoricsCommutative Algebra05C50text