Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview
| dc.creator | Terwilliger, Paul | |
| dc.date | 2003-07-04 | |
| dc.date.accessioned | 2026-07-07T04:59:25Z | |
| dc.date.available | 2026-07-07T04:59:25Z | |
| dc.description | Let $K$ 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. | |
| dc.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0307063 | |
| dc.identifier | http://arxiv.org/abs/math/0307063 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67980 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | Primary 05E35; Secondary 33C45,05E30,33D45 | |
| dc.title | Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an overview | |
| dc.type | text |