title: How to plot the Eigenvalues when solving matrix coupled differential equations in PYTHON?
body: <p>Lets say we have three complex matrices and a system of coupled differential equations with these matrices. </p>
  
  <pre><code>import numpy, scipy
  from numpy import (real,imag,matrix,linspace,array)
  from scipy.integrate import odeint
  import matplotlib.pyplot as plt
  
  
  def system(x,t):
  
      a1= x[0];a3= x[1];a5= x[2];a7= x[3];
      a2= x[4];a4= x[5];a6= x[6];a8= x[7];
      b1= x[8];b3= x[9];b5= x[10];b7= x[11];
      b2= x[12];b4= x[13];b6= x[14];b8= x[15];
      c1= x[16];c3= x[17];c5= x[18];c7= x[19];
      c2= x[20];c4= x[21];c6= x[22];c8= x[23];
  
      A= matrix([ [a1+1j*a2,a3+1j*a4],[a5+1j*a6,a7+1j*a8] ])  
      B= matrix([ [b1+1j*b2,b3+1j*b4],[b5+1j*b6,b7+1j*b8] ])
      C= matrix([ [c1+1j*c2,c3+1j*c4],[c5+1j*c6,c7+1j*c8] ])
  
      dA_dt= A*C+B*C
      dB_dt= B*C
      dC_dt= C
  
      list_A_real= [dA_dt[0,0].real,dA_dt[0,1].real,dA_dt[1,0].real,dA_dt[1,1].real]
      list_A_imaginary= [dA_dt[0,0].imag,dA_dt[0,1].imag,dA_dt[1,0].imag,dA_dt[1,1].imag]
  
      list_B_real= [dB_dt[0,0].real,dB_dt[0,1].real,dB_dt[1,0].real,dB_dt[1,1].real]
      list_B_imaginary= [dB_dt[0,0].imag,dB_dt[0,1].imag,dB_dt[1,0].imag,dB_dt[1,1].imag]
  
      list_C_real= [dC_dt[0,0].real,dC_dt[0,1].real,dC_dt[1,0].real,dC_dt[1,1].real]
      list_C_imaginary= [dC_dt[0,0].imag,dC_dt[0,1].imag,dC_dt[1,0].imag,dC_dt[1,1].imag]
  
      return list_A_real+list_A_imaginary+list_B_real+list_B_imaginary+list_C_real+list_C_imaginary
  
  
  
  t= linspace(0,1.5,1000)
  A_initial= [1,2,2.3,4.3,2.1,5.2,2.13,3.43]
  B_initial= [7,2.7,1.23,3.3,3.1,5.12,1.13,3]
  C_initial= [0.5,0.9,0.63,0.43,0.21,0.5,0.11,0.3]
  x_initial= array( A_initial+B_initial+C_initial )
  x= odeint(system,x_initial,t)
  
  plt.plot(t,x[:,0])
  plt.show()
  </code></pre>
  
  <p>I have basically <strong>two questions</strong>:</p>
  
  <ol>
  <li><p><strong>How to reduce my code?</strong> By reduce I meant, is there a way to do this by not writing down all the components separately ,but handling with the matrices while solving the system of ODE?</p></li>
  <li><p>Instead of plotting elements of the matrices with respect to <strong>t</strong> (the last 2 lines of my code), <strong>how can I plot Eigenvalues (absolute values) (lets say, the abs of eigenvalues of matrix A as a function of t)?</strong></p></li>
  </ol>