Two linear transformations each tridiagonal with respect to an eigenbasis of the other
| dc.creator | Terwilliger, Paul | |
| dc.date | 2004-06-27 | |
| dc.date.accessioned | 2026-07-07T05:09:44Z | |
| dc.date.available | 2026-07-07T05:09:44Z | |
| dc.description | Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy both conditions below: (i) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal, and the matrix representing $A^*$ is irreducible tridiagonal. (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 $V$. Refining this notion a bit, we introduce the concept of a Leonard system. We give a complete classification of Leonard systems. We discuss how Leonard systems correspond to the $q$-Racah and related polynomials from the Askey scheme. | |
| dc.identifier | https://arxiv.org/abs/math/0406555 | |
| dc.identifier | http://arxiv.org/abs/math/0406555 | |
| dc.identifier | Linear Algebra Appl. 330 (2001), 149--203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71693 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | 17B37 | |
| dc.title | Two linear transformations each tridiagonal with respect to an eigenbasis of the other | |
| dc.type | text |