Eigenvectors

Eigenvectors[m]
gives a list of the eigenvectors of the square matrix m.

Eigenvectors[{m, a}]
gives the generalized eigenvectors of m with respect to a.

Eigenvectors[m, k]
gives the first k eigenvectors of m.

Eigenvectors[{m, a}, k]
gives the first k generalized eigenvectors.

Details and OptionsDetails and Options

  • Eigenvectors finds numerical eigenvectors if m contains approximate real or complex numbers.
  • For approximate numerical matrices m, the eigenvectors are normalized.
  • Eigenvectors corresponding to degenerate eigenvalues are chosen to be linearly independent.
  • For an nn matrix, Eigenvectors always returns a list of length n. The list contains each of the independent eigenvectors of the matrix, followed if necessary by an appropriate number of vectors of zeros. »
  • Eigenvectors with numeric eigenvalues are sorted in order of decreasing absolute value of their eigenvalues.
  • Eigenvectors[m, ZeroTest->test] applies test to determine whether expressions should be assumed to be zero. The default setting is ZeroTest->Automatic.
  • Eigenvectors[m, spec] is equivalent to Take[Eigenvectors[m], spec].
  • The option settings Cubics->True and Quartics->True can be used to specify that explicit radicals should be generated for all cubics and quartics.
  • SparseArray objects can be used in Eigenvectors.
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