MATLAB Function Reference |
Convert complex diagonal form to real block diagonal form
Syntax
Description
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.
Examples
has a pair of complex eigenvalues.
[V,D] = eig(X) V = 1.0000 -0.0191 - 0.4002i -0.0191 + 0.4002i 0 0 - 0.6479i 0 + 0.6479i 0 0.6479 0.6479 D = 1.0000 0 0 0 4.0000 + 5.0000i 0 0 0 4.0000 - 5.0000i
Converting this to real block diagonal form produces
[V,D] = cdf2rdf(V,D) V = 1.0000 -0.0191 -0.4002 0 0 -0.6479 0 0.6479 0 D = 1.0000 0 0 0 4.0000 5.0000 0 -5.0000 4.0000
Algorithm
The real diagonal form for the eigenvalues is obtained from the complex form using a specially constructed similarity transformation.
See Also
cd | cdfepoch |
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