Documentation

# rsf2csf

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 ```