I have a parametrical matrix (18x18) which I want to plot its eigenvalues with respect to a parameter. For simplicity, lets assume that it is instead a 3x3 matrix which is not fully numerical but depends on a parameter Y. So that all eigenvalues depend on Y as well. I need to plot all eigenvalues with respect to Y in a single plot (Y in the x-axis). Any suggestions?

In addition, would you please explain if I use Eigenvectors[A] to get eigenvectors (depending on Y), are the result normalized or I need to normalize them myself?

Thank you in advance.

  • 1
    $\begingroup$ Symbolic eigenvectors will not be normalized. $\endgroup$ Commented Dec 15, 2020 at 23:40
  • $\begingroup$ What do you want to plot when some of the eigenvalues are complex? Or is your matrix structured so that they are all real-valued? $\endgroup$
    – bill s
    Commented Dec 15, 2020 at 23:46
  • $\begingroup$ @bills at the end they are all real-valued. $\endgroup$
    – sara sam
    Commented Dec 16, 2020 at 1:15

1 Answer 1

a = {{x, 1 + x}, {1 - x, x}};
eigenvalues = Eigenvalues[a]
Plot[eigenvalues, {x, 0, 1}]

{x - Sqrt[1 - x^2], x + Sqrt[1 - x^2]}

enter image description here


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