# Energy of a symmetric matrix with $0$, $1$ or $-1$ entries

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,

• "energy" is not a standard notion for a matrix. Please provide a link with a definition – Dima Pasechnik Jul 27 '19 at 7:23
• @DimaPasechnik „sum of absolute values of eigenvalues“ is fine as a definition. – Simon1729 Jul 27 '19 at 8:30
• For a symmetric matrix, this ("energy") is just the trace norm of the matrix. – Christian Remling Jul 27 '19 at 18:17