[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 3
0 4 5
0 -5 4
Converting this to real block diagonal form produces[V,D] = eig(X)
V =
1.0000 0.4002 - 0.0191i 0.4002 + 0.0191i
0 0.6479 0.6479
0 0 + 0.6479i 0 - 0.6479i
D =
1.0000 0 0
0 4.0000 + 5.0000i 0
0 0 4.0000 - 5.0000i
[V,D] = cdf2rdf(V,D)
V =
1.0000 0.4002 -0.0191
0 0.6479 0
0 0 0.6479
D =
1 0 0
0 4 5
0 -5 4
eig
,rsf2csf
(c) Copyright 1994 by The MathWorks, Inc.