eigen(x, symmetric=all(x==t(x)), only.values=false) eigen.rs(x, only.values=false) eigen.rg(x, only.values=false)
x
| a matrix whose spectral decomposition is to be computed. |
symmetric
| if true, the matrix is assumed to be symmetric and only its lower triangle is used. |
only.values
| if true, only the eigenvalues are computed and returned, otherwise both eigenvalues and eigenvectors are returned. |
RS and RG.
The functions eigen.rs and eigen.rg provide
versions of the decomposition for the symmetric and
general cases.
They provide a slight performance advantage by skipping
the symmetry test of eigen.
Value
The spectral decomposition of x is returned
as components of a list.
If the eigenvalues are all real the list contains components;
values, a vector containing the eigenvalues of x and
vectors, a matrix whose columns contain the eigenvectors of x.
If some of the eigenvalues are complex, the list contains additional components;
values.im and vectors.im, which respectively contain
the imaginary parts of the eigenvalues and eigenvectors of x.
References
Smith, B. T, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe,
V. Klema, C. B. Moler (1976).
Matrix Eigensystems Routines - EISPACK Guide.
Springer-Verlag Lecture Notes in Computer Science.
See Also
svd, qr.