@misc{10498/32047,
year = {2023},
url = {http://hdl.handle.net/10498/32047},
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.},
publisher = {MDPI},
keywords = {linear operators},
keywords = {pre-Euclidean spaces},
keywords = {graph theory},
title = {Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs},
doi = {10.3390/MATH11030725},
author = {Abdelwahab, Hani and Barreiro, Elisabete and Calderón Martín, Antonio Jesús and Sánchez Delgado, José María},
}