[V,D] = cdf2rdf(V,D)
[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
X = V*D/V
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 span the corresponding invariant vectors.
has a pair of complex eigenvalues.X =1 2 30 4 50 -5 4
Converting this to real block diagonal form produces[V,D] = eig(X)V =1.0000 0.4002 - 0.0191i 0.4002 + 0.0191i0 0.6479 0.64790 0 + 0.6479i 0 - 0.6479iD =1.0000 0 00 4.0000 + 5.0000i 00 0 4.0000 - 5.0000i
[V,D] = cdf2rdf(V,D)V =1.0000 0.4002 -0.01910 0.6479 00 0 0.6479D =1 0 00 4 50 -5 4
eig,rsf2csf
(c) Copyright 1994 by The MathWorks, Inc.