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# Eigensystem

 Eigensystem[m]gives a list {values, vectors} of the eigenvalues and eigenvectors of the square matrix m. Eigensystem[{m, a}]gives the generalized eigenvalues and eigenvectors of m with respect to a. Eigensystem[m, k]gives the eigenvalues and eigenvectors for the first k eigenvalues of m. Eigensystem[{m, a}, k]gives the first k generalized eigenvalues and eigenvectors.
• Eigensystem finds numerical eigenvalues and eigenvectors if m contains approximate real or complex numbers.
• All the non-zero eigenvectors given are independent. If the number of eigenvectors is equal to the number of non-zero eigenvalues, then corresponding eigenvalues and eigenvectors are given in corresponding positions in their respective lists.
• If there are more eigenvalues than independent eigenvectors, then each extra eigenvalue is paired with a vector of zeros.  »
• Eigensystem[m, ZeroTest->test] applies test to determine whether expressions should be assumed to be zero. The default setting is .
• {vals, vecs}=Eigensystem[m] can be used to set vals and vecs to be the eigenvalues and eigenvectors respectively.  »
• The option settings and can be used to specify that explicit radicals should be generated for all cubics and quartics.
Symbolic eigenvalues and eigenvectors:
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Exact eigenvalues and eigenvectors:
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Numerical value:
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Eigenvalues and eigenvectors computed with numerical methods:
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 Scope   (6)
 Options   (2)
 Applications   (2)
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