def california_migration_matrix_eigenvalues ( ):

#*****************************************************************************80
#
## california_migration_matrix_eigenvalues() determines the eigen information.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    19 January 2025
#
#  Author:
#
#    John Burkardt
#
#  Output:
#
#    real L[2]: the eigenvalues.
#
#    real V[2,2]: the eigenvectors.
#
  import numpy as np

  print ( '' )
  print ( 'california_migration_matrix_eigenvalues():' )
  print ( '  Compute eigen information for matrix A' )

  A = np.array ( [ \
    [ 0.70, 0.10 ], \
    [ 0.30, 0.90 ] ] )

  L, V = np.linalg.eig ( A )

  print ( '' )
  print ( '  eigenvalues L: ')
  print ( L )

  print ( '' )
  print ( '  eigenvectors V:')
  print ( V )

  AV = np.matmul ( A, V )
  print ( '' )
  print ( '  A*V:')
  print ( AV )

  VL = np.matmul ( V, np.diag ( L ) )
  print ( '' )
  print ( '  V*np.diag(L):' )
  print ( VL )

  return

if ( __name__ == "__main__" ):
  california_migration_matrix_eigenvalues ( )