 |
BUILT-IN MATHEMATICA SYMBOL
Eigensystem
Eigensystem[m]
gives a list 
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.
Eigensystem[{m, a}, k]
gives the first k generalized eigenvalues and eigenvectors.
Details and Options
- Eigensystem finds numerical eigenvalues and eigenvectors if m contains approximate real or complex numbers.
- For approximate numerical matrices m, the eigenvectors are normalized.
- 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].
can be used to set vals and vecs to be the eigenvalues and eigenvectors respectively. »- Eigensystem[m, spec] is equivalent to applying Take[..., spec] to each element of Eigensystem[m].
- 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 Eigensystem. »
New in 1 | Last modified in 5
