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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.


The matrix

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.

See Also

eig, rsf2csf

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