There is a way to determine the number of real eigenvalues or complex eigenvalues of a non-symmetric real matrix without compute the caluculation?

  • 2
    $\begingroup$ That's at least as difficult as computing the number of real zeros of a real polynomial. $\endgroup$ – Lord Shark the Unknown May 6 '18 at 10:05
  • $\begingroup$ I don't want to perform any calculation. $\endgroup$ – iacopo May 6 '18 at 10:08
  • 1
    $\begingroup$ You want to just stare at the matrix, and have the number of real eigenvalues pop into your head? I think you're being a bit unrealistic, iacopo. $\endgroup$ – Gerry Myerson May 6 '18 at 10:18

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