Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs

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 {Ui}i∈I, each one admitting a basis inherited from B, in such way that f=∑...

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Veröffentlicht in:Mathematics (Basel) 2023-02, Vol.11 (3), p.725
Hauptverfasser: Abdelwahab, Hani, Barreiro, Elisabete, Calderón, Antonio J., Sánchez, José M.
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Sprache:eng
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Zusammenfassung: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 {Ui}i∈I, each one admitting a basis inherited from B, in such way that f=∑i∈Ifi. 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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11030725