gives a list of the eigenvectors of the square matrix m.


gives the generalized eigenvectors of m with respect to a.


gives the first k eigenvectors of m.


gives the first k generalized eigenvectors.

Details and Options

  • Eigenvectors finds numerical eigenvectors if m contains approximate real or complex numbers.
  • For approximate numerical matrices m, the eigenvectors are normalized.
  • For exact or symbolic matrices m, the eigenvectors are not 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, supplemented if necessary with an appropriate number of vectors of zeros. »
  • Eigenvectors with numeric eigenvalues are sorted in order of decreasing absolute value of their eigenvalues.
  • Eigenvectors[m,spec] is equivalent to Take[Eigenvectors[m],spec].
  • Eigenvectors[m,UpTo[k]] gives k eigenvectors, or as many as are available.
  • SparseArray objects can be used in Eigenvectors.
  • Eigenvectors has the following options and settings:
  • CubicsFalsewhether to use radicals to solve cubics
    MethodAutomaticmethod to use
    QuarticsFalsewhether to use radicals to solve quartics
    ZeroTestAutomatictest to determine when expressions are zero
  • The ZeroTest option only applies to exact and symbolic matrices.
  • Explicit Method settings for approximate numeric matrices include:
  • "Arnoldi"Arnoldi iterative method for finding a few eigenvalues
    "Banded"direct banded matrix solver
    "Direct"direct method for finding all eigenvalues
    "FEAST"FEAST iterative method for finding eigenvalues in an interval (applies to Hermitian matrices only)
  • The "Arnoldi" method is also known as a Lanczos method when applied to symmetric or Hermitian matrices.
  • The "Arnoldi" and "FEAST" methods take suboptions Method ->{"name",opt1->val1,}, which can be found in the Method subsection.


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Basic Examples  (3)

Symbolic eigenvectors:

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Exact eigenvectors:

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Numerical value:

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Eigenvectors computed using numerical methods:

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Scope  (8)

Options  (10)

Applications  (2)

Properties & Relations  (2)

Possible Issues  (5)

Neat Examples  (1)

Introduced in 1988
Updated in 2015