Spectral scales and linear pencils
| dc.creator | Pavone, Christopher M. | |
| dc.date | 2005-11-04 | |
| dc.date | 2005-11-09 | |
| dc.date.accessioned | 2026-07-07T06:50:48Z | |
| dc.date.available | 2026-07-07T06:50:48Z | |
| dc.description | Developed in 1999 by Akemann, Anderson, and Weaver, the spectral scale of an $n\times n$ matrix $A$, is a convex, compact subset of $\mathbb{R}^3$ that reveals important spectral information about $A$ \cite{AAW}. In this paper we present new information found in the spectral scale of a matrix. Given a matrix $A=A_1 + iA_2$ with $A_1$ and $A_2$ self-adjoint and $A_2\neq 0,$ we show that faces in the boundary of the spectral scale of $A$ that are parallel to the x-axis describe elements of $σ(A_1,A_2)\bigcap\mathbb{R},$ the real elements of the spectrum of the linear pencil $P(λ)=A_1 + λA_2.$ | |
| dc.description | 6 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0511120 | |
| dc.identifier | http://arxiv.org/abs/math/0511120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104778 | |
| dc.subject | Spectral Theory | |
| dc.subject | Functional Analysis | |
| dc.subject | 15A22 (primary); 47A10 (secondary) | |
| dc.title | Spectral scales and linear pencils | |
| dc.type | text |