|MATLAB Function Reference|
Convert complex diagonal form to real block diagonal form
If the eigensystem
[V,D] = eig(X) has complex eigenvalues appearing in complex-conjugate pairs,
cdf2rdf transforms the system so
D is in real diagonal form, with 2-by-2 real blocks along the diagonal replacing the complex pairs originally there. The eigenvectors are transformed so that
continues to hold. The individual columns of
V are no longer eigenvectors, but each pair of vectors associated with a 2-by-2 block in
D spans the corresponding invariant vectors.
has a pair of complex eigenvalues.
Converting this to real block diagonal form produces
The real diagonal form for the eigenvalues is obtained from the complex form using a specially constructed similarity transformation.