rsf2csf (MATLAB Function Reference)

Convert real Schur form to complex Schur form

[U,T] = rsf2csf(U,T)

Description

The complex Schur form of a matrix is upper triangular with the eigenvalues of the matrix on the diagonal. The real Schur form has the real eigenvalues on the diagonal and the complex eigenvalues in 2-by-2 blocks on the diagonal.

[U,T] = rsf2csf(U,T)

converts the real Schur form to the complex form.

Arguments U and T represent the unitary and Schur forms of a matrix A, respectively, that satisfy the relationships: A = U*T*U' and U'*U = eye(size(A)). See schur for details.

Examples

Given matrix A,

 1     1     1     3
 1     2     1     1
 1     1     3     1
-2     1     1     4

with the eigenvalues

1.9202 - 1.4742i   1.9202 + 1.4742i   4.8121    1.3474

Generating the Schur form of A and converting to the complex Schur form

[u,t] = schur(A);
[U,T] = rsf2csf(u,t)

yields a triangular matrix T whose diagonal consists of the eigenvalues of A.

U =

-0.4576 + 0.3044i   0.5802 - 0.4934i   -0.0197   -0.3428          
 0.1616 + 0.3556i   0.4235 + 0.0051i    0.1666    0.8001          
 0.3963 + 0.2333i   0.1718 + 0.2458i    0.7191   -0.4260          
-0.4759 - 0.3278i  -0.2709 - 0.2778i    0.6743    0.2466    
    
T =

1.9202 + 1.4742i 0.7691 - 1.0772i -1.5895 - 0.9940i -1.3798 + 0.1864i

0 1.9202 - 1.4742i 1.9296 + 1.6909i 0.2511 + 1.0844i

0 0 4.8121 1.1314

0                                               0                  0

1.3474