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Eigensystem

FilledSmallSquare Eigensystem[m] gives a list values, vectors of the eigenvalues and eigenvectors of the square matrix m.

FilledSmallSquare Eigensystem[m, a] gives the generalized eigenvalues and eigenvectors of m with respect to a.

FilledSmallSquare Eigensystem[m, k] gives the eigenvalues and eigenvectors for the first k eigenvalues of m.

FilledSmallSquare Eigensystem finds numerical eigenvalues and eigenvectors if m contains approximate real or complex numbers.

FilledSmallSquare 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.

FilledSmallSquare If there are more eigenvalues than independent eigenvectors, then each extra eigenvalue is paired with a vector of zeros.

FilledSmallSquare Eigensystem[m, ZeroTest -> test] applies test to determine whether expressions should be assumed to be zero. The default setting is ZeroTest -> Automatic.

FilledSmallSquare The eigenvalues and eigenvectors satisfy the matrix equation m.Transpose[vectors] == Transpose[vectors].DiagonalMatrix[values].

FilledSmallSquare Generalized eigenvalues and eigenvectors satisfy m.Transpose[vectors] == a.Transpose[vectors].DiagonalMatrix[values].

FilledSmallSquare vals, vecs = Eigensystem[m] can be used to set vals and vecs to be the eigenvalues and eigenvectors respectively.

FilledSmallSquare Eigensystem[m, spec] is equivalent to Take[Eigensystem[m], spec].

FilledSmallSquare SparseArray objects can be used in Eigensystem.

FilledSmallSquare See notes for Eigenvalues.

FilledSmallSquare See Section 3.7.9.

FilledSmallSquare See also: NullSpace, JordanDecomposition, SchurDecomposition, SingularValueDecomposition, QRDecomposition.

FilledSmallSquare Related package: LinearAlgebra`Orthogonalization`.

FilledSmallSquare New in Version 1; modified in 5.0.

Further Examples