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documentation:language_reference:objects:matrix:functions:eigensystem [2024/12/12 17:27] – Maurits W. Haverkortdocumentation:language_reference:objects:matrix:functions:eigensystem [2025/05/06 14:11] (current) – Maurits W. Haverkort
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 {{indexmenu_n>999}} {{indexmenu_n>999}}
-====== Eigensystem ======+====== Matrix.Eigensystem ======
  
 ### ###
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 <code Quanty Example.Quanty> <code Quanty Example.Quanty>
 A = Matrix.New({{1,1,3}, A = Matrix.New({{1,1,3},
-                {1-2E-10,3,7},+                {1-1E-7,3,5},
                 {3,5,1}})                 {3,5,1}})
 val, funL, funR = Eigensystem(A) val, funL, funR = Eigensystem(A)
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 print("The matrix transformed to a diagonal matrix by its eigenfunctions is\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funR)) ) print("The matrix transformed to a diagonal matrix by its eigenfunctions is\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funR)) )
  
-print("Be carefull, using only the left handed eigenvectors is not sufficient to diagonalize the matrix\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funL)) )+print("The left and right hand vectors are now only marginally different\n",Chop( Matrix.Conjugate(funL) * A * Matrix.Transpose(funL)) )
 </code> </code>
  
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 With potential complex eigenvalues With potential complex eigenvalues
 The eigenvalues are The eigenvalues are
-{ -4.5383431004156 , 0.59104712937687 , 8.9472959710387 }+{ -3.7873476689872 , 0.64886022722351 , 8.1384874417637 }
 The left  eigenfunctions are The left  eigenfunctions are
-{ { -0.3497         , -0.4901         ,  0.8089         } , +{ { -0.3763         , -0.5129         ,  0.7715         } , 
-  { -0.924          ,  0.3964         , -0.0062         } , +  { -0.853          ,  0.5169         , -0.0725         } , 
-  { -0.3429         , -0.6415         , -0.6945         } }+  { -0.3616         , -0.6854         , -0.632          } }
  
 The right eigenfunctions are The right eigenfunctions are
-{ { -0.2791         , -0.6392         ,  0.7283         } , +{ { -0.3763         , -0.5129         ,  0.7715         } , 
-  { -0.8588         ,  0.5199         , -0.0562         } , +  { -0.853          ,  0.5169         , -0.0725         } , 
-  { -0.3174         , -0.7492         , -0.5912         } }+  { -0.3616         , -0.6854         , -0.632          } }
  
 The matrix transformed to a diagonal matrix by its eigenfunctions is The matrix transformed to a diagonal matrix by its eigenfunctions is
-{ { -4.5383 ,  0      ,  0      } , +{ { -3.7873 ,  0      ,  0      } , 
-  {  0      ,  0.591  ,  0      } , +  {  0      ,  0.6489 ,  0      } , 
-  {  0      ,  0      ,  8.9473 } }+  {  0      ,  0      ,  8.1385 } }
  
-Be carefull, using only the left handed eigenvectors is not sufficient to diagonalize the matrix +The left and right hand vectors are now only marginally different 
-{ { -4.6149 , -0.562  ,  0.5784 } , +{ { -3.7873 , -5.4e-8 ,  2.3e-9 } , 
-  {  0.0732 ,  0.5976 ,  0.0395 } , +  {  9.2e-9 ,  0.6489 , -6.7e-9 } , 
-  { -1.1403 ,  0.598  ,  9.0498 } }+  { -4.9e-9 , -8.4e-8 ,  8.1385 } }
 </file> </file>
  

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