2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62161A question of interest in Linear Algebra is whether all n x n complex matrices can be unitarily tridiagonalised. The answer for all n not equal to 4 (affirmative or negative) has been known for a while, whereas the case n=4 seems to have remained open. In this paper, we settle the n=4 case in the affirmative. Some machinery from complex algebraic geometry needs to be used.14 pagesRings and AlgebrasAlgebraic Geometry14H60; 15A21text