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Energy of matrices

Author

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  • Bravo, Diego
  • Cubría, Florencia
  • Rada, Juan

Abstract

Let Mn(C) denote the space of n × n matrices with entries in C. We define the energy of A∈Mn(C) as (1)E(A)=∑k=1n|λk−tr(A)n|where λ1,…,λn are the eigenvalues of A, tr(A) is the trace of A and |z| denotes the modulus of z∈C. If A is the adjacency matrix of a graph G then E(A) is precisely the energy of the graph G introduced by Gutman in 1978. In this paper, we compare the energy E with other well-known energies defined over matrices. Then we find upper and lower bounds of E which extend well-known results for the energies of graphs and digraphs. Also, we obtain new results on energies defined over the adjacency, Laplacian and signless Laplacian matrices of digraphs.

Suggested Citation

  • Bravo, Diego & Cubría, Florencia & Rada, Juan, 2017. "Energy of matrices," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 149-157.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:149-157
    DOI: 10.1016/j.amc.2017.05.051
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    References listed on IDEAS

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    1. Wang, Wen-Huan, 2016. "Ordering of oriented unicyclic graphs by skew energies," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 136-148.
    2. Milovanović, Igor & Milovanović, Emina & Gutman, Ivan, 2016. "Upper bounds for some graph energies," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 435-443.
    3. Monsalve, Juan & Rada, Juan, 2016. "Bicyclic digraphs with maximal energy," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 124-131.
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    Keywords

    Energy of matrices; Energy of graphs;

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