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https://hdl.handle.net/10316/113967
Title: | Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs | Authors: | Abdelwahab, Hani Barreiro, Elisabete Calderón, Antonio J. Sánchez, José M. |
Keywords: | linear operators; pre-Euclidean spaces; graph theory | Issue Date: | 2023 | Publisher: | MDPI | Project: | UIDB/00324/2020 PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banach’ and by the PAI, with project number FQM298 project FEDER-UCA18-107643, and by the Spanish project ‘Algebras no conmutativas y de caminos de Leavitt. Algebras de evolución. Estructuras de Lie y variedades de Einstein’. |
Serial title, monograph or event: | Mathematics | Volume: | 11 | Issue: | 3 | Abstract: | In this work, we study a linear operator f on a pre-Euclidean space V by using properties of a corresponding graph. Given a basis B of V, we present a decomposition of V as an orthogonal direct sum of certain linear subspaces fUigi2I , each one admitting a basis inherited from B, in such way that f = åi2I fi. Each fi is a linear operator satisfying certain conditions with respect to Ui. Considering this new hypothesis, we assure the existence of an isomorphism between the graphs of f relative to two different bases. We also study the minimality of V by using the graph of f relative to B. | URI: | https://hdl.handle.net/10316/113967 | ISSN: | 2227-7390 | DOI: | 10.3390/math11030725 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais I&D CMUC - Artigos em Revistas Internacionais |
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