# Plot the lowest eigenvalues of a parametric matrix

The question here is somewhat related to the comments in Computing eigenvectors and eigenvalues

I have a matrix M, say 400 by 400, and all elements depend explicitly on one parameter t in a quadratic form. That's to say, for one given t, I can calculate each element and write down the full matrix explicitly.

I would like to try different t, say a list of t(s), see how the lowest eigenvalues change with respect to t and plot it. I tried something like assuming and with but it did not work well. Anyone has an idea how to do it efficiently? Thanks.

ClearAll[mat, minev]
SeedRandom
rm = RandomInteger[10, {400, 400, 3}];

mat[t_] := rm.{1, t, t^2};
minev[t_?NumericQ] := Eigenvalues[mat[t], -1];

DiscretePlot[Evaluate[minev[t]], {t, 0, 1, .01}] • Thanks. You always come to my rescue.... May 4, 2016 at 3:07
• @James, i am glad i could help. Thank you for the Accept.
– kglr
May 4, 2016 at 3:08
• by the way, do you think it possible to get the exact coordinates of the points after I plot? Also, is it possible change the scale of y axis after I plot? I know we have lots of options in the plotting function and we can set them before running the plot command. May 4, 2016 at 3:13
• @James, to extract the point coords from dp = DicretePlot[...]; you can use Cases[dp, Point[x_] :> x, {0, Infinity}][]. For the second question, you can use Show[dp, PlotRange->{a,b}] to change the y axis range to {a,b}.
– kglr
May 4, 2016 at 3:20