Plotting Piecewise function?

Question

I am facing a problem in plotting the Piecewise function. I simplified my problem to take the following form:

where \[Sigma][i] are Pauli matrices. My code is:

\[Sigma][1] = PauliMatrix[1]; \[Sigma][2] = 
 PauliMatrix[2];    \[Sigma][3] = PauliMatrix[3];
DM = {{2 t, 0, 0, 8}, {0, 8, 10, 0}, {0, 15, 5, 0}, {2, 0, 0, 3}};
x[i_] = Tr[DM.(KroneckerProduct[\[Sigma][i], \[Sigma][i]])];
X = {{x[1], x[2], x[3]}};
{\[Lambda]1, \[Lambda]2, \[Lambda]3, \[Lambda]4} = Eigenvalues[DM];
MR = Piecewise[{{Tr[DM.DM\[Transpose]] - Norm[X], 
    X != 0}, {Max[\[Lambda]1, \[Lambda]2, \[Lambda]3, \[Lambda]4], 
    X = 0}}]
Plot[MR, {t, 0, 100}] 

Answer 1

In your piecewise definition, you're comparing a vector with a number (zero). This won't work:

{1, 1} == 0
(* {1, 1} == 0 *)

Instead, you need to compare to the zero vector:

{1, 1} == {0, 0}
(* False *)

Also, you had a typo in the piecewise, it should be X == {0, 0} instead of X = {0, 0}, although MMA 12.1 auto-corrected it. Here's the final code that produces a plot:

σ[1] = PauliMatrix[1]; 
σ[2] = PauliMatrix[2]; 
σ[3] = PauliMatrix[3];
DM = {{2 t, 0, 0, 8}, {0, 8, 10, 0}, {0, 15, 5, 0}, {2, 0, 0, 3}};
x[i_] = Tr[DM.(KroneckerProduct[σ[i], σ[i]])];
X = {{x[1], x[2], x[3]}};
{λ1, λ2, λ3, λ4} = Eigenvalues[DM];
MR = Piecewise[{{Tr[DM.DM\[Transpose]] - Norm[X], 
    X != {0, 0}}, 
    {Max[λ1, λ2, λ3, λ4], 
    X == {0, 0}}}]
Plot[MR, {t, 0, 100}]