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arXiv · 2401.12916

Decompositions of linear operators on pre-euclidean spaces by means of graphs

Hani Abdelwahab·Elisabete Barreiro·Antonio J. Calderón·José M. Sánchez
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Abstract

In this work we study a linear operator $f$ on a pre-euclidean space $\mathcal{V}$ by using properties of a corresponding graph. Given a basis $\B$ of $\mathcal{V}$, we present a decomposition of $\mathcal{V}$ as an orthogonal direct sum of certain linear subspaces $\{U_i\}_{i \in I}$, each one admitting a basis inherited from $\B$, in such way that $f = \sum_{i \in I}f_i$, being each $f_i$ a linear operator satisfying certain conditions respect with $U_i$. Considering new hypothesis, we assure the existence of an isomorphism between the graphs associated to $f$ relative to two different bases. We also study the minimality of $\mathcal{V}$ by using the graph associated to $f$ relative to $\B$.

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BibTeXRIS

Hani Abdelwahab, Elisabete Barreiro, Antonio J. Calderón, José M. Sánchez. 2024-01-23. Decompositions of linear operators on pre-euclidean spaces by means of graphs. https://doi.org/10.3390/math11030725

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