Hessenberg Pairs of Linear Transformations
| dc.creator | Godjali, Ali | |
| dc.date | 2008-11-28 | |
| dc.date.accessioned | 2026-07-07T12:08:04Z | |
| dc.date.available | 2026-07-07T12:08:04Z | |
| dc.description | Let $\fld$ denote a field and $V$ denote a nonzero finite-dimensional vector space over $\fld$. We consider an ordered pair of linear transformations $A: V \to V$ and $A^*: V \to V$ that satisfy (i)--(iii) below. Each of $A, A^*$ is diagonalizable on $V$. There exists an ordering $\lbrace V_i \rbrace_{i=0}^d$ of the eigenspaces of $A$ such that A^* V_i \subseteq V_0 + V_1 + ... + V_{i+1} \qquad \qquad (0 \leq i \leq d), where $V_{-1} = 0$, $V_{d+1}= 0$. There exists an ordering $\lbrace V^*_i \rbrace_{i=0}^δ$ of the eigenspaces of $A^*$ such that A V^*_i \subseteq V^*_0 + V^*_1 + ... +V^*_{i+1} \qquad \qquad (0 \leq i \leq δ), where $V^*_{-1} = 0$, $V^*_{δ+1}= 0$. We call such a pair a {\it Hessenberg pair} on $V$. In this paper we obtain some characterizations of Hessenberg pairs. We also explain how Hessenberg pairs are related to tridiagonal pairs. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0812.0019 | |
| dc.identifier | http://arxiv.org/abs/0812.0019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209191 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 15A04, 05E30 | |
| dc.title | Hessenberg Pairs of Linear Transformations | |
| dc.type | text |