This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

EigenvectorsLinearSolve

Eigensystem

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

FilledSmallSquareEigensystem 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.

FilledSmallSquareEigensystem[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 See The Mathematica Book: Section 3.7.9.

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

FilledSmallSquare Related packages: LinearAlgebra`Orthogonalization`, LinearAlgebra`Cholesky`.

Further Examples

EigenvectorsLinearSolve