Author(s): Abdelwahab, Hani ; Barreiro, Elisabete ; Calderón, Antonio J. ; Sánchez, José M.
Date: 2023
Persistent ID: https://hdl.handle.net/10316/113967
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): linear operators; pre-Euclidean spaces; graph theory
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.
