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For a parametrized matrix $H(\lambda)$, how do I plot all the eigenvalues of the matrix vertically corresponding to a particular value of $\lambda$? i.e. we use $\lambda$ as the horizontal axis and the eigenvalues are along the vertically axis.

ps. We can for sure plot each of these points separately, but I'm wondering whether there is a simpler way. Thanks.

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  • $\begingroup$ could you provide a MWE of the input? $\endgroup$ – Nasser Jun 3 at 2:23
  • $\begingroup$ what does MWE stand for? $\endgroup$ – M. Zeng Jun 3 at 4:08
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    $\begingroup$ MWE is a minimum working example that somewhat represents your problem. Having that makes it much easier for people to help you as they don’t have to spend so much time writing code or guessing what you want. In this case, even providing a small sample dataset would be really helpful. $\endgroup$ – MassDefect Jun 3 at 4:31
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    $\begingroup$ Tracking Eigenvalues Through a Crossing $\endgroup$ – LouisB Jun 3 at 4:44
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See if the following works for you (I made up a matrix that depends on lambda since none was provided):

ClearAll[m] 
m[lambda_] := {{1 + lambda,       2 lambda,          3}, 
               {3 + lambda^2,   1 - lambda,          2}, 
               {2,                      -1,   3 lambda}}

DiscretePlot[Evaluate@Eigenvalues@m[l], {l, 1, 10}, Filling -> None]

plot for discrete values of lambda

Plot[Evaluate@Eigenvalues@m[l], {l, 1, 10}]

plot for continuous values of lambda

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