rsf2csf (MATLAB Functions)

Convert real Schur form to complex Schur form

Syntax

```
[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

4.8121    1.9202 + 1.4742i    1.9202 + 1.4742i    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 (underlined here for readability) consists of the eigenvalues of A.

U =

-0.4916       -0.2756 - 0.4411i    0.2133 + 0.5699i   -0.3428
-0.4980       -0.1012 + 0.2163i   -0.1046 + 0.2093i    0.8001
-0.6751        0.1842 + 0.3860i   -0.1867 - 0.3808i   -0.4260
-0.2337        0.2635 - 0.6481i    0.3134 - 0.5448i    0.2466

T =

4.8121        -0.9697 + 1.0778i   -0.5212 + 2.0051i   -1.0067
     0         1.9202 + 1.4742i    2.3355              0.1117 + 1.6547i
     0              0              1.9202 - 1.4742i    0.8002 + 0.2310i
     0              0                   0              1.3474

See Also

schur

rref run