On the matrix equation XA-AX=X^p
| dc.creator | Burde, Dietrich | |
| dc.date | 2004-09-27 | |
| dc.date | 2005-02-23 | |
| dc.date.accessioned | 2026-07-07T06:33:31Z | |
| dc.date.available | 2026-07-07T06:33:31Z | |
| dc.description | We study the matrix equation $XA-AX=X^p$ in $M_n(K)$ for $1< p <n$. It is shown that every matrix solution $X$ is nilpotent and that the generalized eigenspaces of $A$ are $X$-invariant. For $A$ being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for $A^mX^{\ell},X^{\ell}A^m$ and $(AX)^{\ell}$ are given. The case $p=2$ is a special case of the algebraic Riccati equation. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409512 | |
| dc.identifier | http://arxiv.org/abs/math/0409512 | |
| dc.identifier | Linear Algebra and its Appl. 404, 147-165 (2005). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99220 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A24 | |
| dc.title | On the matrix equation XA-AX=X^p | |
| dc.type | text |