MATLAB Function Reference |

Convert real Schur form to complex Schur form

**Syntax**

**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.

converts the real Schur form to the complex form. ```
[U,T] = rsf2csf(U,T)
```

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**

Generating the Schur form of `A`

and converting to the complex Schur form

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**

rref | run |

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