Protected Tag Error [closed]

Question

Consider the following code:

ANCL={{0, 25, 0, 0}, {-((36 k1)/41), -((36 k2)/41), 544/5125, -24.0179}, {(900 k1)/41, 11.6625 k2, -(544/205), -24.5524}, {11.6625 k1, 11.6625 k2, 0.0764667, -2.42273}}
Table[Eigenvalues[ANCL], {{k1, {0.001, 0.01, 0.1}}, {k2, {0.01, 0.1, 1}}}];
p = ListPlot[{Re[#], Im[#]} & /@ %, AxesOrigin -> {0, 0}, 
PlotRange -> {{-5, 0}, {-25, 25}}, ImagePadding -> 40, 
AspectRatio -> 1, Frame -> True, 
FrameLabel -> {{Im, None}, {Re, "complex plane"}}, 
PlotStyle -> Directive[Red, PointSize[.02]]];
Show[p]

I get the error "Tag List in {k1,{0.001,0.01,0.1}} is Protected.".

Now I use Quit[] before starting the evaluation. Also, I am really not defining any functions here. The intention is just to evaluate eigenvalues for varying $k_1$ and $k_2$. I checked the other similar questions but I think I do not have the same issue.

P.S. I edited the code to include ANCL.

Answer 1

There are two problems with the code in question.

• Multiple variables in Table need to be enclosed in separate lists i.e: not Table[expr,{{var1,specs},{var2specs}}] but rather Table[expr,{var1,specs},{var2,specs}]. This is the source of the protected tag error.
• ListPlot needs a list of coordinates {{x1,y1},{x2,y2},...} rather than the matrix provided as an output of Table in order to plot correctly.

With those elements in mind, let me provide you with an alternative visualisation for your problems, using Manipulate:

ANCL[k1_,k2_] := {{0, 25, 0, 0}, {-((36 k1)/41), -((36 k2)/41), 
   544/5125, -24.0179}, {(900 k1)/41,11.6625 k2, -(544/205), -24.5524},
   {11.6625 k1, 11.6625 k2,0.0764667, -2.42273}}

I write the matrix as a function of $k1$ and $k2$ for convenience (don't forget to clear the previous definition of ANCL).

Manipulate[
 ListPlot[
  Transpose[{Re@Eigenvalues[ANCL[k1, k2]], 
    Im@Eigenvalues[ANCL[k1, k2]]}], 
  PlotStyle -> Directive[Red, PointSize[0.02]], Frame -> True, 
  FrameLabel -> {{Im, None}, {Re, "complex plane"}}]
 , {k1, {0.001, 0.01, 0.1}}, {k2, {0.01, 0.1, 1}}]

Or maybe you wanted all the eigenvalues on the same plot, in which case:

ListPlot[Flatten[
  Table[Transpose[{Re@Eigenvalues[ANCL[k1, k2]], 
     Im@Eigenvalues[ANCL[k1, k2]]}], {k1, {0.001, 0.01, 
     0.1}}, {k2, {0.01, 0.1, 1}}], 2], 
 PlotStyle -> Directive[Red, PointSize[0.02]], Frame -> True, 
 FrameLabel -> {{Im, None}, {Re, "complex plane"}}]

Be mindful of the level specification ($2$) in the argument of Flatten.

Edit: With differenciated eigenvalues and tooltips!

ListPlot[MapThread[
  Tooltip, {Flatten[
    Table[Transpose[{Re@Eigenvalues[ANCL[k1, k2]], 
       Im@Eigenvalues[ANCL[k1, k2]]}], {k1, {0.001, 0.01, 
       0.1}}, {k2, {0.01, 0.1, 1}}], 1], 
   Map[ToString, 
    Flatten[Table[{k1, 
       k2}, {k1, {0.001, 0.01, 0.1}}, {k2, {0.01, 0.1, 1}}], 1]]}], 
 PlotStyle -> Directive[PointSize[0.02]], Frame -> True, 
 FrameLabel -> {{Im, None}, {Re, "complex plane"}}, 
 PlotLegends -> 
  SwatchLegend[
   Map[ToString, 
    Flatten[Table[{k1, 
       k2}, {k1, {0.001, 0.01, 0.1}}, {k2, {0.01, 0.1, 1}}], 1]], 
   LegendLabel -> Text["{k1,k2}"]]]