0
$\begingroup$

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,

$\endgroup$
3
  • 2
    $\begingroup$ "energy" is not a standard notion for a matrix. Please provide a link with a definition $\endgroup$ – Dima Pasechnik Jul 27 '19 at 7:23
  • 1
    $\begingroup$ @DimaPasechnik „sum of absolute values of eigenvalues“ is fine as a definition. $\endgroup$ – Simon1729 Jul 27 '19 at 8:30
  • 1
    $\begingroup$ For a symmetric matrix, this ("energy") is just the trace norm of the matrix. $\endgroup$ – Christian Remling Jul 27 '19 at 18:17
2
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.