Documentation

This is machine translation

Translated by Microsoft
Mouse over text to see original. Click the button below to return to the English verison of the page.

cdf2rdf

Convert complex diagonal form to real block diagonal form

Syntax

[V,D] = cdf2rdf(V,D)

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

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 spans the corresponding invariant vectors.

Examples

The matrix

X =
    1     2     3
    0     4     5
    0    -5     4

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

More About

collapse all

Algorithms

The real diagonal form for the eigenvalues is obtained from the complex form using a specially constructed similarity transformation.

See Also

|

Introduced before R2006a

Was this topic helpful?