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Eigenvalues and EigenVectors of a General Matrix
Syntax eigen(x)
eigen(x,e)
[e,d] = eigen(x)
See Also eig , geneig , eigsym , symeig , schur , svd

Description
Computes the eigenvalues of the matrix x, where x is a square real, double-precision or complex matrix.

If the return value d is not present, the return value of eigen is a complex column vector, with the same row dimension as x, containing the eigenvalues of x. If the return value d is present, it is set to a complex diagonal matrix with the same dimension as x and with the eigenvalues along its diagonal.

If the argument e is present the eigenvectors of x are also computed. The input value of e does not matter and its output value is a complex matrix containing the eigenvectors. It has the same dimension as x. Each of the columns of e has norm one; i.e., for j between 1 and the row dimension of x
            __________________________
     1 =   /       2                2
         \/ e(i, 1)  + ... + e(i, n)
where n is the row dimension of x.

The eigenvalues and eigenvectors satisfy the equation
     e * d = x * e

Example
If you enter
     x  = {[1., 1.], [2., 2.]}
     [e, d] = eigen(x)
     print e, d
 O-Matrix will respond
     {
     [ (0.447214,0) , (-0.707107,0) ]
     [ (0.894427,0) , (0.707107,0) ]
     }
     {
     [ (3,0) , (0,0) ]
     [ (0,0) , (2.22045e-016,0) ]
}
Mlmode
In Mlmode , this function is called eig instead of eigen. If in Mlmode you enter
     x  = [1., 1.; 2., 2.]
     eig(x);
 O-Matrix will respond
     { 
     (3, 0) 
     (0, 0) 
     }