2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67980Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider an ordered pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy conditions (i), (ii) below. (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal. (ii) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal and the matrix representing $A^*$ is irreducible tridiagonal. We call such a pair a Leonard pair on $V$. We give an overview of the theory of Leonard pairs.14 pages, 1 figureRings and AlgebrasCombinatoricsPrimary 05E35; Secondary 33C45,05E30,33D45text