%0 Journal Article 
%A Abdelwahab, Hani
%A Barreiro, Elisabete
%A Calderón Martín, Antonio Jesús
%A Sánchez Delgado, José María
%T Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs
%D 2023
%@ 2227-7390
%U http://hdl.handle.net/10498/32047
%X 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.
%K linear operators
%K pre-Euclidean spaces
%K graph theory
%~ Universidad de Cádiz