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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