2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223470We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n by n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.26 pages, 2 tables and 2 figures. To appear in Linear Algebra and Its ApplicationsCommutative AlgebraRings and Algebras15A33; 15A18; 16R30text