MATLAB Function Reference |

**Syntax**

**Description**

The `schur`

command computes the Schur form of a matrix.

```
T = schur(A)
```

returns the Schur matrix `T`

.

```
T = schur(A,flag)
```

for real matrix A, returns a Schur matrix `T`

in one of two forms depending on the value of `flag`

:

If `A`

is complex, `schur`

returns the complex Schur form in matrix `T`

. The complex Schur form is upper triangular with the eigenvalues of `A`

on the diagonal.

The function `rsf2csf`

converts the real Schur form to the complex Schur form.

```
[U,T] = schur(A,...)
```

also returns a unitary matrix `U`

so that `A`

= `U*T*U'`

and `U'*U`

= `eye(size(A))`

.

**Examples**

`H`

is a 3-by-3 eigenvalue test matrix:

The eigenvalues, which in this case are `1`

, `2`

, and `3`

, are on the diagonal. The fact that the off-diagonal elements are so large indicates that this matrix has poorly conditioned eigenvalues; small changes in the matrix elements produce relatively large changes in its eigenvalues.

**Algorithm**

`schur`

uses LAPACK routines to compute the Schur form of a matrix:

**See Also**

**References**

[1] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra,
J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen,
*LAPACK User's Guide*
(http://www.netlib.org/lapack/lug/lapack_lug.html), Third Edition,
SIAM, Philadelphia, 1999.

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