2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58253We construct six multi-parameter families of Hermitian quasi-exactly solvable matrix Schroedinger operators in one variable. The method for finding these operators relies heavily upon a special representation of the Lie algebra o(2,2) whose representation space contains an invariant finite-dimensional subspace. Besides that we give several examples of quasi-exactly solvable matrix models that have square-integrable eigenfunctions. These examples are in direct analogy with the quasi-exactly solvable scalar Schroedinger operators obtained by Turbiner and Ushveridze.Latex, 19 pagesMathematical PhysicsHigh Energy Physics - PhenomenologyAnalysis of PDEsQuantum Physicstext