Plotting eigenvalues in one plot for three different parameters

Question

I am trying to plot eigenvalues of the matrix with different $W$. I can plot them separately but I want to merge them in a single plot with different colors. Is there any other type of plot other than Listlineplot?

The code is

x = Sqrt[M/2];
y = -Sqrt[M/2];
W = M/2 (A + τ) + B;
M = 2;

P = {{A x^2 + τ*y^2 - W, B}, {B, A y^2 + τ*x^2 - W}};
Q = {{-3*A* x^2 - τ*y^2 + W, -2 τ*x*y - B}, {-2 τ*x*y - B, -3* A* y^2 - τ*x^2 + W}};

T[A_, τ_] := P.Q

ListLinePlot@Flatten@Table[
     Eigenvalues[T[A,τ]]
     , {A, 0, 1, 0.3}
     , {B, 0, 1, 0.3}
     , {τ, 0, 1, 0.3}
 ]

Second plot is for

W = M/2 (A + τ) - B;

Third one for

W = A*M;

I also tried to Manipulateplot but the outcome is empty.

Answer 1

Module[
 {x, y, W, M, P, Q, T, wlist},
 x = Sqrt[M/2];
 y = -Sqrt[M/2];
 wlist = {M/2 (A + τ) + B, M/2 (A + τ) - B, A*M};
 M = 2;
 P = {{A x^2 + τ*y^2 - W, B}, {B, A y^2 + τ*x^2 - W}};
 Q = {{-3*A*x^2 - τ*y^2 + W, -2 τ*x*y - B}, {-2 τ*x*y -
      B, -3*A*y^2 - τ*x^2 + W}};
 T[A_, τ_] := P.Q;
 ListPlot[
  Table[
   Flatten@Table[
     Eigenvalues[T[A, τ]]
     , {A, 0, 1, 0.3}
     , {B, 0, 1, 0.3}
     , {τ, 0, 1, 0.3}
     ]
   , {W, wlist}
   ]
  , PlotStyle -> Array[Hue, 3, {0, 0.7}]
  , Joined -> True
  , PlotTheme -> "Scientific"
  , AspectRatio -> 1/2
  , ImageSize -> 600
  , PlotRange -> All
  , PlotLegends -> TraditionalForm /@ wlist
  ]
 ]