In Maple, Mathematica, and MATLAB, how do I obtain eigenvalues and eigenvectors?

Maple

In Maple, in the LinearAlgebra package, the command to obtain eigenvalues and eigenvectors for the matrix A is:

  Eigenvectors(A)

For example:

  > with(LinearAlgebra): 
  > A:=<1, 2; 6, -1>;
       [1     2]
  A := [       ]
       [6    -1]
  > v,e:=Eigenvectors(A);
         [  1/2 ]  [    2            2     ]
         [13    ]  [---------    ----------]
  v, e := [      ], [  1/2           1/2    ]
         [   1/2]  [13    - 1    -13    - 1]
         [-13   ]  [                       ]
                   [    1            1     ]
  > evalf(v);
  [3.605551275 ]
  [            ]
  [-3.605551275]

Mathematica

In Mathematica, use:

  {v, e} = Eigensystem[A] 

For example:

In[1]:= A = {{1, 2}, {6, -1}}                                             

Out[1]= {{1, 2}, {6, -1}}

In[2]:= {v, e} = Eigensystem[A]                                           

                                  1 - Sqrt[13]       1 + Sqrt[13]
Out[2]= {{-Sqrt[13], Sqrt[13]}, {{------------, 1}, {------------, 1}}}
                                       6                  6

In[3]:= N[v]                                                              

Out[3]= {-3.60555, 3.60555}

MATLAB

In MATLAB, use:

  [e,v] = eig(A)

For example:

>> A=[1, 2; 6, -1]
A =
     1     2
     6    -1
>> [e v]=eig(A)
e =
    0.6089   -0.3983
    0.7933    0.9172
v =
    3.6056         0
         0   -3.6056
>> v
v =
    3.6056         0
         0   -3.6056

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This is document afko in the Knowledge Base.
Last modified on 2015-05-20 00:00:00.

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