Eigensystem
 Usage
• 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.
Notes
• 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. • Eigensystem[m, ZeroTest -> test] applies test to determine whether expressions should be assumed to be zero. The default setting is ZeroTest -> Automatic. • The eigenvalues and eigenvectors satisfy the matrix equation m.Transpose[vectors]  Transpose[vectors].DiagonalMatrix[values]. • Generalized eigenvalues and eigenvectors satisfy m.Transpose[vectors] a.Transpose[vectors].DiagonalMatrix[values]. • {vals, vecs} = Eigensystem[m] can be used to set vals and vecs to be the eigenvalues and eigenvectors respectively. • Eigensystem[m, spec] is equivalent to Take[Eigensystem[m], spec]. • New in Version 1; modified in 5. • Advanced Documentation.
| 
