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I have a symmetric matrix with entries $0$, $1$ or $-1$ which appeared in my works in graph theory (the diagonal entries are all zero). I need a good upper bound for the energy of this matrix; i.e. "the sum of the absolute values of its eigenvalues". Can anybody help?

Bests,

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    $\begingroup$ "energy" is not a standard notion for a matrix. Please provide a link with a definition $\endgroup$
    – Dima Pasechnik
    Commented Jul 27, 2019 at 7:23
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    $\begingroup$ @DimaPasechnik „sum of absolute values of eigenvalues“ is fine as a definition. $\endgroup$
    – Simon1729
    Commented Jul 27, 2019 at 8:30
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    $\begingroup$ For a symmetric matrix, this ("energy") is just the trace norm of the matrix. $\endgroup$
    – Christian Remling
    Commented Jul 27, 2019 at 18:17

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This survey on the energy of graphs includes some bounds which seem useful, although without a more specific question it's difficult to pick out particular ones.

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