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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.  »
  • {vals, vecs}=Eigensystem[m] can be used to set vals and vecs to be the eigenvalues and eigenvectors respectively.  »
  • The option settings Cubics->True and Quartics->True can be used to specify that explicit radicals should be generated for all cubics and quartics.
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